Looks like all my woes with HDMI were due to bad cables and microHDMI adapters. I’ve used Raspberry Pi microHDMI output as a reference, thinking that if it works on Raspberry Pi and stable - it should work on Pocket.
Turns out that assumption was incorrect. Pocket seems to be quite a bit more sensitive to cable/adapter quality. When I replaced my cable and adapter with some premium ones - all issues went away, it’s been rock solid for few hours. I even switched to QHD@144Hz and it still works great.