Hi,
That's great you have the hardtop, a unique option. You have a 64 keep an eye on eBay as the brochures come up frequently. There are subtle trim/ interior differences to tell correct year, where yours is untouched you should be able to tell with high confidence.
Anyways to the transom question. The only way to tell is to poke into the transom core and see what's in there.
Where motor bolts are rusted there is a slim chance transom is OK but, I highly doubt it, this is a good indicator water infiltrated the wood core. Poke into the bolt holes try to probe in there, hard white wood is good, darker soft is bad. Blue is probably silicone someone added later in the boats life. Where your interior and gel are OK this means the boat probably was covered and well cared for, meaning it is likely the foam under the floor is OK. Transoms on these are relatively easy to fix, under floor foam is not, so I'll bet you have an excellent easily repaired Edinboro on your hands.
After dissecting a few of these to do needed repairs some manufacturing deficiencies are evident. As a side note MFG's are wonderful hulls and built pretty tough, yours is one of the compression molded steel tooled die variety, worth reading about in the catalogs available in that section of this web site. It has all glass strigers and floors, the only wood is behind the dash and in the transom.
The transoms have multiple construction boo,boos but, are very typical of every glass boat I've restored.
It's important to understand the weaknesses so they can be corrected.
Look at the places where water will wick into the wood, that is the transom top, no sealer or caulking, it's an aluminum strip over essentially the bare edge of the wood core. Screws holding the trim are not sealed either. The drain plug tubes are pushed into a tight fitting drilled hole, no sealers of caulking, water will wick into the core between the tube and the drilled hole. Motor bolt holes, speedo pitot tubes etc. all penetrate into the wood. Usually these are not eagled well.
All this is easily corrected. MFG's are easy transom jobs, motor well un bolts so deck does not have to come off.
Cut floor about 8 inches ahead of transom to gain access to transom below the floor. The MFG transoms are curved for strength so it's best to laminate several thinner layers of plywood to follow the contour rather than thicker more difficult to bend panels. The are hundreds of opinions and methods to read on the site. I use
epoxies and marine plywood and mostly biaxial stitched cloth for such repairs. I did a 64 Edinboro a few years ago. I liked it so much I looked for a larger MFG and now have a 65 Erie. You can PM me for rebuild specifics if you want, just let me know your phone number.
Anyways you have a very good example worth investigating and repairing if needed.
Don't be bummed if you have a repair needed the boats are 50 years old and time and trapped water wins. We have all had the disappointment but, also the thrill of rebuilding and correcting issues for many future years of worry free boating.
Randy