If you find a "mid-time" engine, do you plan on just hanging it on your plane and fly the remaining time on that engine?
Purchasing an engine "as removed" has risks, as you can only go by what the seller tells you about it. You may never get the true story on how it was operated and maintained.. The biggest question on this type of engine is WHY was it removed? Most folks don't just remove a running engine off an airplane unless something happened. Yes, there are "wind damaged" planes, and yes, maybe a truck plowed into the plane on the ground.....
If you decide to get a used engine ( no matter what you think, it will be USED) make sure it has logbooks. Installing a different engine on your plane means you get a new set of engine logs from that engine.
Personally, I would rather put the $4000-$5000 money you would pay for a used mid time engine toward the overhaul of the one you currently have. I know it sucks having your plane down, but renting in the interim would probably be cheaper than buying a 2nd engine.