While researching this issue further, I stumbled across a post on Lemon64 which is suggesting the shimmering/wiggling issue is related to a certain MOS VIC-II chip variant 8565R2
I tested a RetroTINK 2X today. It loses horizontal sync on the 8565R2 after 40 seconds. I tested two chips from different factories and two monitors. Always goes wiggly after 40 seconds.
It worked on a 6567R8, 6569R3, and a newer 8565 (forgot which one and not going to open case). The 6560 works too. So it’s just one chip version that’s a problem, which happens to be a very popular chip.
Link to thread: https://www.lemon64.com/forum/viewtopic.php?t=69472
I opened up my C64 Reloaded Mk2 and it does indeed have the 8565R2 installed (with LumaFix64), I just checked my spares and I fortunately have a 6569R3 so I’m going to swap this out and I will report back (might be next week somepoint with Xmas and my shift pattern).