Tranny help.. Starting in 3rd

[Burnout]

So I didn't get around to changing my transmission last weekend, some things got in the way, but that means I'm currently stuck with a half to non working car. Figured I'd ask to see if maybe the transmission thats in there isn't completely shot, and maybe I can get a few more miles out of it.

Let's say I start it on a cold morning and go for a drive. In S3/S4 and D it'll start in third. If I put it into 2, it'll switch to 2. Now once the transmission warms up, it'll start slipping, completely missing third, and half the time wont go into second, sometimes it'll start going but when you apply gas it'll just start revving (this is in 2). So I was thinking torque converter problems maybe?

Any ideas on how I can extend the life of this transmission far enough to get me around while I try and get around to changing it out?

Here's what I've done:
Cleaned the soleniods, I think. I took all four out, cleaned them with brake cleaner, then tested them the best that I knew how (they all made a very faint clicking and popping. It wasn't loud, but I wasn't sure if it was supposed to be or not? I figured since they all made nearly the same exact sound, they were all working fine). The little metal filters, particularly on the shifting soleniods, were pretty full of gunk, as well as some noted metal particles ( bad sign).
I also changed the transmission fluid. Now I think this may have something to do with the large problems I'm having now. I changed the fluid because it was shifting harder than normal and having some problems in third. Upon changing the fluid (before cleaning the solenoids) my problems went away, it was shifting smoother and wasn't having a problem in third. Drove to Florida and back without any incidents and everything. Then a few weeks after I got back, the problems started again, and then they got worse, to the point I am at now. I didn't use Honda ATF (the nearest Honda / acura dealer is a bit of a drive away), but I did use what I thought would be the most compatible. Maybe this is my problem?