If you're going to use a 727, why are you even asking about manual transmission flywheels?
Torque convertors are trans. specific- 904 v.s. 727, 10" v.s. 11"; and no, you can't use a lockup convertor on a standard 3 spd. non-L.U. automatic. The input spline splines are completely different.
What you do need:
Two ways you can go-
1.) Get a factory flexplate and externally balanced torque convertor for an LA 360/727 combo, either 10 or 11", but the flexplate and TC need to match. All LA360s use the same external balance. Don't even think about using Magnum 5.9 parts on it.
2.) Get any internally (neutral) balanced torque convertor for a 727, and use the B&M 10236 flexplate, which takes the LA360 balance into consideration.
DO NOT mix and match any parts between 1.) and 2.) !!
And make sure your 727 is for a smallblock, not a big block.