I have a couple of questions that may save you some serious grief.
How are the stringers and the floors? It would be very unusual to have concentrated wood rot just in the transom. To do the transom properly, the stringers, portions of the floor and the motor mounts need to be removed and redone.
I have done literally hundreds of these and can say with a 90% certainty that the transom is likely the small problem. Doing this type of work is exactly how I almost lost my left hand (long story).
I highly recommend having some serious exploratory investigation work done. When I do these, all through cut areas like exhaust holes, bilge pump dumps, trim tab holes, get drilled out to a much larger size and Sea Going Epoxy is used to fill and re-drill the holes, this make the wood getting wet an absolute improbability.
In most cases (depending on labor rates and materials used), this was a $2500 plus job.
If someone gives a quote for less than $2K, get it in writing. These things have the tendency to take on a life of their own.
Lifted 250, please do not take that personally, this sounds like an I/O, not a jet, quite complex comparatively speaking. I am in the middle of doing my Carerra Elite and I have 18 hours in it just removing the old wood. I use a time clock to have an idea of what jobs take, I will have well over 60 hours in this one. Figure that out at your local shops labor rate.....

GT