I'm running a trans cooler with a dedicated fan attached to it, full synthetic ATF and stock new(well, new when I rebuilt the trans. Not the same Original stock) torque converter. No heat issues even in 100 degree days. As for gearing, I'm on 37" BFG's and 3spd trans, samurai t-case with 6.5 gear set in it and 5:38's in my axles.
Torque converters wear out. Not very expensive to replace them. They wear out, fluid gets super heated quickly, then shortly after that, kills transmission either from failed fluid, temps or debris from falling apart TQ. Don't be a cheap ass and leave the stock one with 130,000+ miles on it and expect it to last. (just a general statement to all those thinking of this kind of swap).
As for the slop, The splines on the transmission should be fairly tight and not move much at all. If you able to move things around with the intermediate shaft in there, then its the splines in the slip that are worn. You still should be OK, but may seep some fluid out of the seal every now and then. Just have to keep an eye out for a less mileage track/kick to get another slip yolk out of. You'll notice most stockers are sloppy after 80K miles.