340 Engine Shake
At this point I think anything will help. :) I can't speak to the balancing though. The machine work was done so long ago, that I just don't remember and I don't have the sheet. Those pictures of the block and crank were taken in 2012
I think reposting your videos would help the crowd. I doubt it's a balancing issue, mostly because it seems to idle smooth then 'surge' occasionally. There's quite a few settings in the Fitech which can have an effect on this. I fought the same thing, and had put it down to my cam for a long time - but after lots of fine tuning, I was able to nearly eliminate it.
Maybe try going back into the idle control, and you should find 'idle trim jump' both pos and neg. Cut them in half or reduce them by 1/3 and see if it helps. The way AFR control works in closed loop is for the computer to 'jump' the mixture, then trim it across the target. So for instance, if you program the idle AFR as 14.5, it'll jump to 14.1, then reduce fuel with each rev until it hits say 14.8, then jump back to 14.1 - these are just made up numbers, reality they're much smaller. It does this rather than try to 'chase' an idle AFR setting back and forth. When the jump setting is large, the swing in AFR can be come excessive and cause headaches. Too small though, and your idle can become unstable.
If you leave the key on for ~45 seconds, your AFR should go from 14.7 to 20+. The heater in the O2 has to warm up the sensor before it reads properly. Heat from the engine can also warm it up, but if it never leaves 14.7 after key-on (without starting), the sensor may be bad.
Since the EFI isn't showing a change in vac or AFR or anything, I'd hook up a vacuum gauge and see what there is to see. The way the engine changes revs and shakes, I expect the vacuum is actually changing. Lots of Fitech units have been known to have a bad seal of the MAP to the throttle body. There's
lots of videos and discussion forums which tackle the issue.