The cost to modify one of these airplanes with an upgraded engine is crazy right now. Dave Stoots will answer your questions, give him a call, leave a message, he'll get back to you. Ask him what that price of the STC includes. Generally, the cost of a current STC typically is not just the paperwork. It includes proprietary parts as well, like an engine mount. And, STC or not (ie: if you go to Experimental/Exhibition category), you still have to come up with those parts from somewhere, and often, the only source is the holder of the STC. Parts such as engine mount, exhaust, cowling mods (if needed), plus an engine, propeller, etc, etc.
So, IF you were to go with a Lycoming O-360, for example, I doubt if you can find one of those engines in decent shape for less than say, $50K. Add $15K plus for a prop, plus other accessories (look up some pricing on things like starters and alternators, oil coolers, etc, etc) and you're going to have well north of $70 BEFORE you hire someone to do the work (around here, good mechanics are charging $120/hour), and that's going to be well north of 100 hours, I'd bet.
And, my understanding is that the STC to install the Continental IO-360 engine in the 175 is still available. I'm guessing those engines MAY be a little cheaper and easier to come by than Lycomings. Maybe.
Again, understand that even if you call it Experimental, you'll have most of the cost in the plane anyway, but the value of the plane likely will suffer at resale. Oh, and by the way, the FAA is pretty lenient in the Experimental Exhibition and Airshow category at the moment, but that category has been "discovered" by quite a few folks, and it wouldn't surprise me a bit for the FAA to crank down on the provisions of that category. If that happens, you are essentially screwed.
My understanding is that the GO-300 CAN be overhauled today. Do some research, make some calls. That is the way to go, frankly. Either that or purchase one that's already converted. I see a few occasionally needing some love selling for "reasonable" prices.
Whatever you do, stay far, far away from a guy named Williams, who currently owns the AVCON engine conversion. IF you can get in touch with him, he MAY sell you paper, but I wouldn't bet that you'll ever see that paper. Beware.
This is from the owner of a 1958 Cessna 175, with AVCON engine conversion and Bolen tailwheel conversion. Mine was already converted when I bought it. I've also put a lot of $$ into it in upkeep and repairs.