I hear a lot of good suggestions that I will try, and hopefully one of them will work.
When I bought my Shark, I thought I was buying a top-quality machine -- apparently that's not really the case, which is why I was so sure the results from the Axiom would be so much better. if you haven't seen one, there is NO flex. The cutter runs side-to-side on the gantry on a pair of dovetailed splines that keep the cutter from bouncing. The fact that the Axiom gave me the same results tells me that machine flex is not the issue. And even tho the gcode is different between the Shark and the Axiom, I could be looking at an issue with how the gcode is generated ( i.e. a software problem ).
To highpocket's point, I'm not exactly sure how the Axiom sets Z0, but you can use a "touch off puck" similar to the Shark's touchpad. However, unlike the Shark, I don't think the puck is placed on the wood. I think it's placed somewhere else on the table. My friend talked about a "table origin" versus a "project origin". One of my thoughts was that if there any fuzz under my touchpad when I changed bits, that would throw off Z0. But it would cause the second cut, the detail cut, to cut more shallow, not deeper. So I scratched that as a root cause.
TReischl: are you suggesting that I only make that finish cut with the clearance tool, and make the detail cut normally?
Mobius: Point #2: again, since I got the same results on both the Shark and the Axiom, I'm not sure it this is applicable. It certainly could be, but I don't see how. And it doesn't mean I won't look into it anyway.
Point #3: No, they are not the same type of tool. My 3/16" clearance bit it is an up-cut spiral bit, but my very first attempt was with a straight, two-fluted bit. Something else to consider ...
Point #4: One of the reasons I take it a little slower and don't hog out too much at a time is to prevent exactly what you're describing. With the 3/16" bit I'm using a cut depth of 1/8", which that bit should be able to handle easily. With the 1/16" bit, I only take 1/16" at a time.
Point #6: I use four clamps on the corners to hold everything down. If this only happened with cuts in the middle, I'd think I'd need to use some double-sided tape just for insurance. But this piece is only 4" tall. As for thickness, the last piece was 3/4".
Point #7: I go from one cut to the next ASAP. Only once did I go more than about 30m, and that was because the first cut didn't finish until about 03:00.
Many things to try. Again, thanks for all your input. What I think would be at least a little telling is if someone else tried to cut that project as-is, and if they saw the same thing.