Seen this scenario before.....
If you really don't want to be doing this again then do it right this time.
1 Strip and clean it again buy a paper and rubber kit their cheap.
2 Replace the filter use a Dacron one. Change to a screen later if you like.
3 (Assuming its not a lockup TC) Flush it out,pour a lil solvent in, put the fwd drum and spin it a few times then dump or better yet suck out the solvent repeat again.
4 Get a can of cooler flush their cheap too... Flush those lines and rad with it !!
5 Air check.... you should hear a solid apply with very slight air leakage. Very hard to judge with little experience so that will be your judgement call.
6 If you use teflon rings, grease them in... They don't air check too well when greased in tho. Personally i prefer the steel rings (User preference).
7 Make sure the pump halves are lined up.. use a large hose clamp with the pump Oring off. Pump will install better in the case when lined properly.. Less possibility of " broken Rings "
8 New fluid..... I know its tempting but DONT reuse the old fluid.
Last of all ..Haste makes waste
And... Why is there never enough time to do it right, BUT ALWAYS enough time to do it again.... Think about it Good luck