That should clean up very well. The wrap around seat stays were used on nishiki competition-I don't know that Amer Eagle had a model name. TMar (Nishiki Guru ) started this serial database. The KS in the # means early 70's. The stem looks like an earlier compe stem/maybe late 60's?
The crankset however looks newer. Report your progress and give a ride report. You sure can conquer some hills with that freewheel! Trek has a site of date codes for some components-google 'dateing vintage bicycle components' and it should come up.