Scott, something doesn't seem right. Last year I had a similar experience at a remote site. An isolated pier I poured was integrated into the slab by what must have been your contractor idiot's brother. Not only that, he made a 14 foot by 14 foot slab into a 7 by 17 foot slab. (Father in law uses the guy and they misunderstood his instructions they said.) But anyway, what's done is done.
I setup my C-11 on a Takahashi NJP mount and had another CN member setup his C-11 on an AP-1200 + Piertech on the same small slab with me. I had the NJP mounted on the pier integrated into the slab. They were constantly walking about (two 200 pounders) and I never saw vibrations.
At home I have the 10' ProDome (looks like yours is the next size up) built on the top floor of a 4 story building. The pier goes through to the floor below but will still jiggle some when the floor is stomped in the observatory. When I image or do high power visual I live with a little vibration. Nothing I can do with the observatory I have will fix it (within reason).
If it were me, I'd take it a little further before sawing up the floor. First, I'd setup the LX200 near or over the Piertech on it's tripod. Then cut the heater on. while carefully observing at high power with the heater on note the vibrations. If you still have the vibrations while using the tripod then while watching Mars or Saturn at high power while seeing the vibrations cut the LX200 drive motors off. I'm quite sure you are seeing a harmonic of some sort and not a physical vibration.
When you rotate a ProDome that is a lot of mass with wierd acoustics. Mine would vibrate a slab while rotating. I note you use the motors for rotation. Those motors have a significant current draw when in operation. There is just a lot of things going back to the power in what you describe. Cut off the PC and the vibration changes. Cut off the fan and it changes. Rotate the dome and you see vibrations. Note all these relate to power loading. A pc motor on 6 yards of concrete with a LX200 at 400 power just doesn't have enough energy to vibrate that setup. I just don't think the problem is isolated yet.
If you still have the vibration on the tripod do one more test. Move the tripod outside the observatory and setup on the ground. Run a drop cord into the dome plugging into the trip outlet (what a contractor) and plug the LX200 into the cord. Have somebody rotate the dome, cut the PC on and off and cycle the heater. If you stil have the vibration outside the dome then...... don't cut the floor.
Before spending a lot of money I'd put a mount in there designed for solid performance. I didn't get good vibration free performance until going with a Takahashi NJP and eventually to the AP-1200. My LX200s always vibrated at high power. A Tak NJP mount will cost you less than the modifications you propose (especially with the contractor experts you are dealing with) and if it still vibrates then at least you have a mount worthy of your observatory (not knocking the Meade, I have one too).
-------------------- Jerry
LX200ACF 14", Tak FS 152 & TOA 150
AP-1200 & Mach1