That my friend is a $100 transmission. First, don't be too concerned with the play in the output shaft. The input shaft of the tranfer case locates the output shaft of the transmission so it will have some excessive play when they are apart. Exactly how much water was in the pan? If you feel it got in the valve body, then there is a problem as the small springs that load the shift valves are not in any way corrosion resitant. If they rust, they are ruined. Is that pieces of aluminum in the pan? The only pic tht concerns me is the water and metal pieces in the pan.
How many miles? 44k mi? Since a build or 44K mi since original?
If it is from original, remember that the seals have better than 10 years of age on them.
To replace the seals in most automatics you will need a piston return spring compressor, various snap ring pliers. The cheap convertable ones will be a major hinderance.
You will need trans assembly lube, and a parts washer that is 99% clean minimum. Feeler gauges, and possibly some special tools that are specific to the a372. (The FSM should outline what you will need.)
If I was in your shoes, I would decide if you really want to do this yourself. I would really consider having someone build it and either give a warranty, or give a good price break for a carry in. Call your local Mitsu dealer and ask them who builds their transmissions for them. It's all in what you want. And knowing how you like to do things, I would not put that one in as is.
BTW Frank, I have a Ford 4R70W that has a burnt up convertor and need a complete overhaul under my bench right now (It's mine) I would not take less than $150 for it "as is". Usually trans shops will buy core transmissions for $100 to use for parts. I wish I would have been paying closer attn to how much you were paying for it before you did. Still anything can be fixed.