It may be too late to do this but I would suggest having the transmission serviced; meaning change the fluid and removal of the pan., With the pan off one can see if there is any debris or excess grunge from the clutches and then make a decision about a possible transmission replacement.
Your guy “thinks” it may be the converter and suggests replacing the transmission. That seems like a pretty expensive thought at this point.
I drive Fords for the most part and find that they’re kind of touchy regarding aged transmission fluid. If fresh fluid and a new filter does not cure it at least you’re not into it for more than a couple or 4 hundred dollars; all depending upon locale, shop rates, and so on.
As for the uneven tires the cause of that could be whatever depending upon the wear pattern. The problem here is that the new tires are also going to wear unevenly.