You need to look at the HDRIVE and VDRIVE signals with an oscilloscope and see whether both of them - or just VDRIVE - is jittery on the oscilloscope.
My guess would be only the VDRIVE signal is affected - in which case it gives us a place to look - being H8 and G10 on
http://www.zimmers.net/anonftp/pub/cbm/schematics/computers/pet/2001N/320349-6.gif (but this is pure supposition at this moment until you get us a measurement).
Are any of these ICs socketed I am asking myself?
The other thing I observed on your 'jumping jack video' is that not all of your ROM checksums are returning correctly! ROM D for example is returning 0000!
Do you have all of the correct ROMs in the PET (apart from the EDIT ROM socket that contains my PETTESTER) and do the checksums match what is in my PETTESTER manual for the version of BASIC you are running?
Try not to replace the ROMs too many times, you may (read will) damage the IC sockets... Leave the PETTESTER in place and get as much information from it as possible - especially the DRAM memory test, ROM checksums and keyboard test.
If a ROM is dead - this will cause the BASIC to enter the debug monitor. Also, if PIA C7 is dead - this will cause the same behaviour. PIA C7 is also involved with the keyboard. So testing the keyboard with the PETTESTER is a good idea...
Dave