My approach: The location of where the corrosion ate threw the transom, I would gently remove the cancer, without making it bigger. Emery cloth with some grit and patience. Work the area, and remove the rust and corrosion. The other areas, I would go with the Disco #541-778-4 4" Wheel Brush - (equivalent to #120 grit) - small wire brass brush around bolt holes.
Do interior and exterior. Clean both sides with DAWN DISH SOAP. Wipe down with either white Vinegar or aliumuim brightner. Clean up with clean rag. Clean the area(s) with Acetone. When dry and temperatures correspond with label, apply MARINE TEX (14 oz container) at a 5 parts resign to 1 part catalyst. Spread this mixture with a Pudy knife or 5" body spreader over the area, and beyond where the corrosion ate threw. Do this on both sides, in a thin layer (1/16 - 1/8) thickness. Let it harden, sand if needed , and a second coat at the same thickness. On the exterior side, make a template of the transom, but only as deep (down) as the interior was - and the same width as the boat. Use a 1/8" aliumium #6061 cut to match template, for your exterior. You will need to do the same with interior side (width and height is determined by what was there) - this should somewhat correspond with the exterior. Now that the MARINE TEX is smoothed to desired shape and thickness and hardened on inside. Clean with a damp cloth. Take a tack cloth, and wipe down. Prime with RUSTOLEUM ETCHED PRIMER (spray) 2 coats allowing drying time between coats on interior and exterior. (THIS PRIMER WILL HELP STOP NEW CORROSION). When temperature is above 50°, paint 2 coats of RUSTOLEUM #7715730 Protective Enamel - 1/2 pt oil based aluminum. Paint over the area where the wooden transom would be mounted on interior, and where new aliumium plate will be installed on the exterior.
When all is covered good in two coats .... time to add back your new transom on the interior. After the transom is installed, add the new 1/8 aliumium plate for your final on exterior and interior - making a sandwich between your wooden transom.
Not knowing what paint you will be using (if any) for Your final exterior coat; primer is only sprayed where new aliumuim is covering the exterior transom. [STEEL FLEX WILL NOT ADHIRE TO ETCHED PRIMER - per Distributor].
Regarding wood transom - do not use marine grade, or ground contact - plenty of info in "TINBOATS " relating to that subject.
Regarding hardware: stainless needs a barrier between it and aliumium. (Neoprene washer, or 3M 5200, will act as a barrier)
If Your not using the bolt holes that are aready in place, use J.B. weld, and plug them, cure and sand. - (GOOGLE WILL HELP)
Making new hardware water tight - use 3M 5200 (permanent epoxy) vs 3M 4200 (non permanent) - (GOOGLE WILL HELP)
There are brighter minds on this site, and those that have been doing this longer than I. Looking forward to their ideas too.