I had similar experience with my gear. The mount was broken when I bought it, and we replaced with the new motor mount and gear legs. I checked the alignment and it was spot-on, but still would get the shimmy unless my landing technique was PERFECT.
SO I put the wood stiffeners on, I did front and back with Maple, and I let in the round with a router, and even put a channel down the leading edge for my brake lines.
All was great after that, but I had a couple of hard landings in gusty conditions and ended up finding the wood had cracked. I ground the glass out and wrapped it again, but I think the wood being partially un-bonded is still causing a periodic shimmy, mostly as I slow (using brakes) after putting the tail down and approaching the runway turn out.
I need to pull the wheel pants and leg fairings off again and see if I can figure out what needs to be done, but that means jacking the plane up and all that fun stuff.
Feel your pain brother....The round gear legs are more susceptible to shimmy than other types, I wish I could say I nail my landing every time, but I don't. Just part of the RV game I guess.
My RV-3 is more fun on accident than your Cessna is on purpose