That is precisely why wood transoms are bad for aluminum boats. I've seen that same view a bunch of times, and it's never a good thing.
Only thing I'd do in that case is cut out the entire transom sheet, and weld in a new one. I'd then go back in with an all aluminum transom. In that case, having the entire sheet out gives you (or your welder) some great design options on the new transom.
The only other way to go about that would be to sand out ALL of the corrosion. Procedure for this would involve sanding over the whole inside and outside surface with a brown scotchbrite on an angle grinder, then taking a die grinder w/ carbide bur, and gouge out ALL of the pits that were untouched by the flat sander. Emphasis on all - if you leave some, it will continue growing. At that point, you can either weld up ALL the pits (alright, not a reasonable option at all), or skin the transom with a new sheet.
Simply skinning the transom without thoroughly removing the corrosion will result in the existing corrosion spreading to the new sheet - until the poultice cells are removed, they aren't going to stop. I don't really recommend skinning the transom, even if you do thoroughly clean all the poultice cells, in that the double layer is just asking for crevice corrosion in the future.
Back to the idea of cutting out the transom sheet, as it's the only one I'd recommend. Basically, I'd cut the new transom piece while the boat is still in it's current shape. Much of the boats shape is held by the transom, so you'll want the new one to be a perfect match. I'd also weld the new transom structure onto the transom sheet on the bench. The time is significantly less doing it now than it would be to install the structure in the hull.
Then, I'd brace the aft section of the hull, flip it over, and cut the after 1/4-3/8" of the hull off. This just eliminates all the existing transom, as well as the original weld bead. Gives you a nice clean edge, without the fuss of working around an existing weld, etc.
At this point, it would be the simple matter of welding in the new transom. That joint would be an outside corner, and that weld would be TIG. Reinstall knee braces and other accessories, and you'll be good to go, permanently.
I don't know what your welder was planning on doing, and my suggestion certainly isn't a 'cheap' fix, but it is really the only long term 'right' way to repair it. Your transom has reached the point of 'too far gone,' so there aren't many other options to make up for the structural deficiency you currently have.
All that being said, that repair, while not cheap, still isn't going to come close to the value of the boat, so it is a very real option on bringing a boat in this condition back to life.