Two Different Times Although, as you note, that there are some similarities between these two prophecies, there is a determining difference, and that is the all important CONTEXT! The prophecy of ch. 8 dealt with the history of Israel through the Persian and Greek era, represented by the Ram and Goat respectively.
But ch. 11-12 dealt with the history of Israel from Persia all the way through the Roman empire to the end of the Jewish nation. It covered the whole SECOND TEMPLE ERA. It relays the history of Persian kings...to the conquest of Alexander the Great ...to the break-up of that empire into four sections...to the rise of Antiochus Epiphanes and the Maccabees...to the Roman conquest of the East...to Herod the Great...to the final Destruction of Judea by the Roman generals and the Zealots!
Daniel 8 Although there is some minor debate over the exact terminus a quo and terminus ad quem of the 2300 days, there is a majority consensus that it deals with the desecration of the Temple and the rededication of it, which is celebrated by the Jews as the Feast of Lights (John 10:22) (See 1 Maccabees 4:41-58, 2 Macc. 10:1-7, Josephus Antiquities 12.7.6-7) The dedication happened on December 25, 165 B.C. So this 2300 time period would represent approximately 171-165 B.C. (6 years, 4 months, 20 days).
Evenings and Mornings One ought not be confused at the terminology of evenings and mornings. Recall that Genesis 1 referred to a single day by the same way. Note also the tendency to divide daylight from night-time in other phrases: forty days and forty nights and three days and three nights, etc. These all were referring to just the number expressed as a whole day. No need for any "calculating, multiplying, configuring, etc. It's just 2300 days at issue here. As far as considering a "year-day" (a year for each day), take note of John Calvin's comment:
It cannot be used of either years or months...those who receive it of years and months are wretchedly mistaken, and even ridiculous in their calculations...We see this altogether foreign and adverse to the mind of Christ, and to the use of this prophecy...We have shown how impossible it is to explain this peophecy otherwise than by Antiochus...Boys even know this by reading the accredited history of those times... (Calvin Commentaries, Daniel, p.541)
Daniel 11-12 The time period of Daniel 11-12 covers the entire SECOND TEMPLE ERA ending with the final Destruction of the Temple. The final verses of it are quoted by Jesus in the Olivet Discourse (12:1, 11) The horrible distress at the fall of Judea was not only referred to by Jesus, but also, the general, Flavius Josephus (See Introduction, Jewish Wars).
According to the synoptic section in Luke the Abomination of Desolation (...that makes desolate) was the Roman Legions (Luke 21:20). And the number of day that the armies tromped up and down the land of Judea was 1290! Recall that Jesus warned His disciples to flee JUDEA, not just Jerusalem. (Matt. 24:16) The devastation was wide-spread with villages being torched in Galilee, Perea, Galilee, and Judea proper, with all supply lines cut off from Jerusalem. When the soldiers finally beseiged Jerusalem their fate was sealed, literally.
The 1335 Days The horrible conquest, with all its suffering, can be read in the history of the eye-witness, Gen. Josephus (A captured Jewish general). We focus rather on the 1330 number of days.
The city of Jerusalem had its three walls of defense breached. The Temple was burned and torn down. The people were massacres, or enslaved. Except for a Herodian palace in the Upper City which refused to surrender. It is estimated they had enough supplies to last for an indeterminate period of time. The walls were so thick and foreboding that the Roman general Titus decided to wait it out.
But amazingly on the 1335th day, the remaining Zealots opened the gates and surrendered mysteriously! Notice the remarks of Josephus' history concerning Titus's surprise:
Now when Titus came into this (upper city), he admired not only some other places of strength in it, but particularly those strong towers which the tyrants in their ad conduct had relinquished; for when he saw their solid altitude, and the largeness of their several stones, and the exactness of their joints, as also how great was their breadth, and how extensive their length, he expressed himself...'We have certainly had God for our assistant in this war, and it was no other than God who ejected the Jews out of these fortifications; for what could the hands of man or any machines do towards overthrowing these towers? (Wars, VI, 9:1)
If the tyrants had stayed in the fortress, the Roman Legions would have stayed around the territory and continued to massacre the Jewish people. The soldiers had seen the despicable display of gross murder the Zealots committed on each other and the citizens, and they had no mercy for them. But as Jesus said, with the mysterious surrender, the killing stopped:
And except those days should be shortened, there would no flesh be saved, but for the elect's sake those days shall be shortened. (Matthew 24:21-22)
Conclusion So it can be concluded, with amazement at the accuracy of biblical prophecy, that the two different Days in Daniel 8 and Daniel 12 refer two separate events. The first one described the desolation by Antiochus and the Dedication of the Temple (instigating the Feast of Lights)...and the second number amazingly portrayed the exact duration of the Desolation of Judea, culminating in the destruction of the Temple!