I know the Thompson Gas Check bullets were given existing mold numbers when Lyman/Ideal bought the designs from Ray Thompson in the early 1950's.
The old molds were given new numbers. The only one I'm sure of is the #429215 became the #429478, a 210gr RN.
As far as I know, My Dad was loading the #358429 in .38Spl cases for .38-44 loads as a teenager in the late 1930's. He never loaded much for the #358446, don't know why He didn't like it. We only had 1 2cav mold for it.
He loaded the #358429 in .357Mag cases by crimping over the front driving band.
Once the #358156 became available, that was His only Bullet of choice for Hot Loads in the .357Mag.
He did load a few 180gr FP's, that's were I got My Saeco #354 mold from. But only for Rifle loads.
I've looked at #358446 & #358156, don't see that the #156 is a gas check copy of the #446.
The driving bands are different on both. Guess you have examine both side by side, good clean castings, unsized.