Sneaky engine vibes have been the hobbyist diagnostician's bane since the dawn of the combustion engine. I'm no expert, other than being able to type:
Definitely find a shop with a Chadwick or comparable prop balancer device, and make sure they know how to use it by using the word "ips" gratuitously and seeing how they respond. If they know lower is better, then they're competent.

You should get a dynamic prop balance either way. They can make what you thought was a smooth engine even better.
I suspect your problem though is different if it's in that narrow RPM range. It could easily be ignition or fuel delivery. Those two things suffer the most variables and potential for wackiness.
I had a magneto once that had a tick/vibe to it that was only noticeable at full power. R&R and it was good as new.
Spark plugs are life limited and will often fail slowly and with some vibration at certain RPM. I had a plug go bad once, not just fouled, but something fundamental like a cracked insulator or something... it felt like the engine was throwing a rod, but only in a narrow RPM range.
Sometimes the magic that routes the atomized fuel into cylinders can cause an imbalance. Carbs need a little TLC now and then. The Cessna 170 used to have a venturi AD if I remember correctly. But I don't remember the exact details.
Just have to start trying stuff and use process of elimination.