Well - - I think I've raised the bar for myself for future DIY builds and know the goal from the beginning.
It took me over 3 hours and the final iteration of work ended up essentially such that I could have boiled it down to two steps:
1) Lay down veneer over entire frame
2) Sand down high spots
I did it piecemeal, but by the end that's what I basically did. I have one 3" area near the center with a gap of around .03" and less than .024" (.6 mm) everywhere else (didn't see how much I have less than .012" etc) - using playing cards as feeler gauges calibrated with a digital Starrett caliper. You can tell it's not perfectly flush in areas by shining a flashlight underneath but that is the only way this can be detected (there's no other visual or physical cues), and also all the corners are flush.
There never was any "rock" from the beginning so I am skeptical of the advice people give others to see if the tank rocks from corner to corner - mine didn't budge a little bit but I still feel like it was way worse before now that I see what I think "good" is supposed to look like.
My other tank set-up on a commercial stand has much bigger and longer gaps then I now have on this one.
Bittersweet - another night where I feel like I discovered a problem and took a long time to correct it, delaying completion of the project ... But satisfied that I have made a much better project. It may have added nothing, or it may have added weeks/months/years/decades to the life of a tank which will be on the stand.
Actually a delay of two nights because I need to stain the parts I sanded and the veneer - but, come this weekend, a tank should be on the stand permanently and I'll be leveling the whole ordeal in my living room. Unless the sig other wants the tank against a different wall, and she'll be back from her trip before I can say "It's too late to move it!"