Rebuilt 360, excessive oil consumption

You need to do a compression test and then find a local guy who can do a leak-down. Things it could be: leaking intake gasket, broekn rings, poor ring seal due to finish or dirt, bad guides in the heads.

My vote is either the first or last choice of what Moper listed, but to me, the first is very likely. I had a similar problem for a while, about a quart in 500 miles or less. I pulled the intake and found cyl number six port was oily and the intake gasket was slightly cracked. Replaced the gasket and the problem was solved.

Do you see any blue smoke coming out of either of the pipes during decelleration after jumping on it? This is a sign of a possible intake gasket issue.

Do a compression check, if possible, first.