low budget bracket racing blues
Here's my take on this. First, you didn't say how old or how fresh the engine is, if you did I missed it. The ring seal could be going away. It would be evident that the car runs better when hot.
Secondly I don't use a cooler on my race car trans and I leave off a tranzbrake. The car is more consistent without it. Just put a temp gauge in the pan. B, or whatever number we are on, yes you need an extension on the filter and lastly, without a cooler you need to run a good synthetic fluid whether it's dexron or type F. I don't use type F personally as it decreases the stall speed of the converter a little but it shouldn't hurt it.
Oh and as long as the engine is running putting it in neutral won't hurt anything on the return road, it's still being lubed. I have shut my engine off and coasted innumerubal times and there is no appreciable wear on the rear support.