If you plan to stay with a stock 14" tire, then leave the 4L60E behind (especially if you plan to upgrade to an LS later), use the TH350 and be a smiling 3 speed owner.
Keep in mind, that the 4.3 is turd no matter what's behind it, so IMO attempting to make that more driveable is a fruitless option. When the LS goes in, install a mild cam with headers and it won't care if you have a TH350 behind it. And lastly, you let someone else grenade the 4L60E. The 4L60E is almost underrated for a stock 5.3 - any hop up in a 5.3 or a stock 6.0 and the 4L60 will be found in smaller pieces than originally installed.