Foremost, the verse quoted by you comes from the Masoretic Text and is probably corrupted. In the Septuagint and also the Samaritan Pentateuch, which are both older than the MT, it reads:
40 And the sojourning of the children of Israel, while they sojourned in the land of Egypt and the land of Chanaan, [was] four hundred and thirty years. (Septuagint)
40 Now the sojourning of the children of Israel and fathers of them, who dwelt in Canaan and in Egypt, was four hundred and thirty years. (Samaritan Pentateuch)
So our first conclusion is that 430 years does not only apply to Egypt but also Canaan.
The second step would be to establish when the period of 430 started. In the Letter to Galatians, in the third chapter, Paul says:
16 The promises were spoken to Abraham and to his seed. Scripture does not say “and to seeds,” meaning many people, but “and to your seed,” meaning one person, who is Christ. 17 What I mean is this: The law, introduced 430 years later, does not set aside the covenant previously established by God and thus do away with the promise. 18 For if the inheritance depends on the law, then it no longer depends on the promise; but God in his grace gave it to Abraham through a promise. 19 Why, then, was the law given at all? It was added because of transgressions until the Seed to whom the promise referred had come.
So the period of 430 years started when Abram was 75 years old and when the promises of Genesis 12 and 15 were made. Isaac was born when Abraham was 100, 25 years after the promises were made. Jacob was born when Isaac was 60. Jacob and his family arrived in Egypt when he was 130. (25+60+130=215) So the time the Israelites spent in Egypt was 215 years. (430-215=215)
This is what Josephus states in the Antiquities of the Jews 2.15.2:
They left Egypt in the month Xanthicus; on the fifteenth day of the Lunar month; four hundred and thirty years after our fore-father Abraham came into Canaan. But two hundred and fifteen years only after Jacob removed into Egypt. It was the eightieth year of the age of Moses, and of that of Aaron three more. They also carried out the bones of Joesph with them, as he had charged his sons to do.
The 400 years of Genesis 15:13 started probably on the day Isaac was weaned.
As for the time of the enslavement, Joseph lived 110 years. His family arrived in Egypt when he was 39. So for the next 71 years, he took care of his family. 215-71=144 The enslavement started sometime after the death of Joseph, so it was definitely less than 144 years. Moses was born when the Israelites were already slaves. So the enslavement was definitely longer than 80 years since it ended when Moses was 80.
In Genesis 46, Kohath is named among the seventy who went down to Egypt.
These are the names of the sons of Israel who went to Egypt: … The sons of Levi: Gershon, Kohath and Merari.
Then in Exodus 6, we are told that Kohath lived 133 years and his son Amram 137.
The sons of Kohath were Amram, Izhar, Hebron, and Uzziel. Kohath lived 133 years. Amram married his father’s sister Jochebed, who bore him Aaron and Moses. Amram lived 137 years.
We know that Moses was 80 when the Israelites left Egypt.
So even if somehow Kohath was a newborn baby when he went down to Egypt, and had Amram the same year that he died, and Amram had Moses just before he died, it gives us only 350 years. 133+137+80=350 In reality it was less than that. Let's keep in mind, that we are talking about the total time they spent in Egypt, not the time of their enslavement.
I just checked the rabbinic commentaries and this is what they say:
And the days of the dwelling of the sons of Israel in Mizraim were thirty weeks of years, (thirty times seven years,) which is the sum of two hundred and ten years. But the number of four hundred and thirty years (had passed away since) the Lord spake to Abraham, in the hour that He spake with him on the fifteenth of Nisan, between the divided parts, until the day that they went out of Mizraim. And it was at the end of thirty years from the making of this covenant, that Izhak was born; and thence until they went out of Mizraim four hundred (years), on the selfsame day it was that all the hosts of the Lord went forth made free from the land of Mizraim. (Targum Pseudo-Jonathan)
FOUR HUNDRED AND THIRTY YEARS. From the day that their father Abraham left the land of his birth. (Ibn Ezra on Exodus 12:40:2)
ומושב בני ישראל אשר ישבו במצרים, “and the habitation of the Children of Israel during which they dwelled in Egypt, etc.” We find three separate sets of numbers for the ending of the exile and subsequent departure from Egypt. They are either 400 years, 430 years, or 210 years. The 400 years are calculated from the time Avraham’s descendants became strangers and experienced various problems either within the land of Canaan or outside of it. This was the fulfillment of the prophecy in Genesis 15,13: “they will serve them or even oppress them for 400 years.” These 400 years include both periods of being strangers and periods of being slaves. The 430 years are calculated since the birth of Yitzchack. [This is hard to understand though it appears in various manuscripts. Ed.] The 210 years refer to the length of the Jews’ stay in Egypt proper. (Rabbeinu Bahya, Shemot 12:40:1)
ומושב בני ישראל אשר ישבו במצרים, we find in connection with the redemption from Egypt 3 different dates of termination all of which relate or appear to relate to the same event. The numbers are: “400 years,” i.e. the prediction in Genesis chapter 15 to Avraham; we find the number 430 years in our verse here. Finally, we have the number 210 years. In order to reconcile these numbers we must remember that the number 400 refers to the time from the birth of Yitzchok. Seeing G’d’s promise to Avraham concerned “his descendants,” any count could not begin until Avraham had such descendants, i.e. Yitzchok. G’d had told him that his descendants would be known through Yitzchok, (not through Ishmael or the sons of Keturah) The number 430 begins with the date when Avraham had been told about his future by G’d at the covenant between the pieces in chapter 15 in Genesis. The number 210 were the years during which Avraham’s descendants were not free men living in what would become their own country in the future. During the latter 86 years of these 210 years they were cruelly enslaved and abused. During the first 124 years of their stay in Egypt, until the death of the last surviving brother of Joseph they enjoyed freedom in Egypt. (Rabbeinu Chananel on Exodus 12:40:1)
שלשים שנה וארבע מאות שנה FOUR HUNDRED AND THIRTY YEARS — Altogether from the birth of Isaac until now were 400 years, and we must reckon from that event, for only from the time when Abraham had offspring from Sarah could the prophecy (Genesis 15:13) “Thy offspring shall be a stranger” be fulfilled; and there had been 30 years since that decree made at “the convenant between the parts” until the birth of Isaac. It is impossible to say that this means that they were 430 years in the land of Egypt alone, for Kohath was one of those who came into Egypt with Jacob (Genesis 46:11); go and reckon all his years and all the years of Amram his son and the whole eighty years of Moses, the latter’s son, until the Exodus and you will not find that they total to so many; and you must admit that Kohath had already lived many years before he went down to Egypt, and that many of Amram’s years are included in the years of his father Kohath, and that many of the 80 years of Moses are included in the years of his father Amram, so that you see that you will not find 400 years from the time of Israel’s coming into Egypt until the Exodus. You are compelled to admit, even though unwillingly, that the other settlements which the patriarchs made in lands other than Egypt come also under the name of “sojourning as a stranger” (גרות), including also that at Hebron, even though it was in Canaan itself, because it is said, (Genesis 35:27) “[Hebron] where Abraham and Isaac sojourned”, and it says, (Exodus 6:4) “[the land Canaan], the land of their sojournings wherein they sojourned”. Consequently you must necessarily say that the prophecy, “thy offspring shall be strangers… [four hundred years]” began only from the time when he had offspring. And only if you reckon the 400 years from the birth of Isaac will you find that from the time they came into Egypt until the time they left it, was 210 years (as alluded to in Genesis 15:13). (Rashi on Exodus 12:40:1)