You may or may not be handy, but perhaps you know someone who is. In my city there is a fully equipped wordworking shop where you can go in and use everything, and they have everything big to small. I can't remember what they want but it seems to me $25/hour rings a bell. Maybe there is something like that where you live?
An alternative might be to just cut out the back panel, maybe leave 2~3 inches along each side, go in and do the appropriate bracing, etc, then add a new back panel sized to the outside dimensions. By screwing in the back panel (into the 2~3 inches you left of the original) instead of permanent adhesive, you can always access the insides of the cabinet to modify bracing, stuffing, etc. In my experience you want to be able to adjust any stuffing in conjunction with listening tests anyway, so it's not really a bad idea all around. Latex caulking (which is paintable) will provide a seal if you feel it's necessary and that is easily removable when necessary and you could just re-apply when you button everything up.
Fixing the out-of-round speaker baffle isn't a difficult job with a beer and some sandpaper and/ or a rasp, assuming there is enough "meat" to mount your driver in the routed hole. No need to get crazy, it will be hidden by the driver mounting flange anyway. If the routed area is also out-of-round, consider a grille cloth, etc.
If "perfect" is already not possible, at least functional is, without starting over, perhaps.
The photos don't look like the work of the cabinet makers I know, but maybe he's just a kitchen / bathroom guy who covers everything up with veneers and laminates and gets his doors and cabinets in a box from some factory.. I had a buddy and the two of use built some awesome speakers but he was a "finish carpenter" which is like a cabinet maker but only does kitchens and bathrooms and built-in cabinets in high end homes. Lower Units kind of like yours but with open baffle mid / tweeter in a separate half-cabinet on top. Apart from the size, they were very good sounding.
You really want someone who builds furniture out of solid wood, they get things like braces and flush corners right.
