The significance seems to be אֵצֶל אֵלֹונֵי מֹרֶֽה, "by the terebinths, (or oaks) of Moreh:"
Both are on the other side of the Jordan, beyond the west road that is in the land of the Canaanites who dwell in the Arabah - near Gilgal, by the terebinths of Moreh? (JPS)
The mountains are the general landmarks, the terebinths of Moreh, the specific location. That is, simply saying Mount Gerizim and Mount Ebal would allow the Israelites to set up anywhere in the valley, but Moses wants them specifically by the terebinths of Moreh.
This seems to set up a type of reenactment of Abram's arrival in Canaan:
1 Now the LORD said to Abram, “Go from your country and your kindred and your father's house to the land that I will show you. 2 And I will make of you a great nation, and I will bless you and make your name great, so that you will be a blessing. 3 I will bless those who bless you, and him who dishonors you I will curse, and in you all the families of the earth shall be blessed.” 4 So Abram went, as the LORD had told him, and Lot went with him. Abram was seventy-five years old when he departed from Haran. 5 And Abram took Sarai his wife, and Lot his brother's son, and all their possessions that they had gathered, and the people that they had acquired in Haran, and they set out to go to the land of Canaan. When they came to the land of Canaan, 6 Abram passed through the land to the place at Shechem, to the oak of Moreh. At that time the Canaanites were in the land. 7 Then the LORD appeared to Abram and said, “To your offspring I will give this land.” So he built there an altar to the LORD, who had appeared to him.
(Genesis 12 ESV)
Abram left Haran as the LORD instructed. His first stop in Canaan was עַד אֵלֹון מֹורֶה, at the terebinth (singular) of Moreh. There the LORD promised the land to Abram's offspring.
Moses instructs the Israelites to return not to the general vicinity between the two mountains, but to the same location where the LORD first promised to give Abram's offspring the land.
This reenactment is in the reverse order of the original events:
A: I will bless those who bless you and curse those who curse you
B: Abram arrives at the oak of Moreh and builds an altar
B': The Israelites arrive at the oaks of Moreh with the Ark of the Covenant
A': The Israelites pronounce blessings from Mt Gerizim and curses from Mt Ebal