The intermittent nature and the fact that a small nudge to the tank can solve it suggests to me it’s hardware (contacts or electrical). It sounds like you already made sure the spring fingers and your tank contacts are clean.
If the printer is idle and you slide the tank back and forth gently, do you get any “tank removed / inserted” messages?
If you have a multimeter you can use it to diagnose the connection between the spring finger and the end of your heater cable like I did in the first part of this post: Form 2 Heater Cable Repair.
I had an intermittent connection problem that often showed up when the tank moved, and in my case it was a bad cable.
Also be sure to contact Support if you haven’t already; they’ll probably give you a guide “Adjusting the Spring Fingers”.
A properly working printer does not have the problems you’re seeing.