Jonboat.
H4350 is a good powder for the 243 in general. I start with 43g with the 85gr bullet. But I think you would get better results with H4831 SC. It will give you good velocities with a lower initial pressure spike since the powder is a lot slower burning. This is of benifit specially in a Handi with its rather loose latch lock up. Also the case is too small for max vel with this powder and bullet weight.
One other powder is Reloder 22 for the 243. Both these powders fill the case which enhances accuray. In bolt guns I use these powders with a slight compression. Reloder 22 is a super performer in the big 6mm's with
85-105gr bullets.
I tried a compression load in the Ultra 25-06 and 85gr match bullets with outstanding results using H1000 and a magnum primer. Fred M.