What you need is a dinghy repairer who has a warm, dry building to do the repair in. A consult with Achilles or a good dinghy repairer will get you the info which glue to use.
The process is to undo the glue and dinghy fabric
, and then, (you having provided the epoxy-saturated and painted or varnished transom) they can re-attach the transom for you, and I would expect that to hold up well. It is important to control both the humidity and the temperature. [Dinghies look awfully big in your living room!]
If you're going to try and do it yourself, one thing we have found quite useful when using contact cements, is ordinary waxed paper, that you keep between the surfaces, then ease out when it is aligned correctly, sticking it together little bit by little bit till you have the whole area bonded.
There might be some info on U Tube, or you could check an inflatable
boat repair book out of a library.
Good luck with it.