LACs/universities with average scores in the ~1250-1300 range include:
Bucknell
Gettysburg
Lafayette
Bard
Dickinson
Sewanee
Boston U
Wisconsin
Florida
Texas
Colorado Mines
UCSB
Some of these places do offer merit scholarships.
Gettysburg for example gives them to 36% of undergrads without need, according to Kiplinger’s. Dunno how many of them are full-tuition (or more). The average amount at Gettysburg is under $14K.