My contractor just finished installing a pre-finished engineered floor from Carlisle Wide Plank during our condo renovation (installed on a wood subfloor over concrete) and there is significant overwood on many of the short edges.

The contractor's floor installer initially raised the issue (although it was obvious when we first got to inspect it) and claims that the issue is a significant milling problem and that we need to completely refinish the floors if we don't want to constantly feel the overwood and risk damaging the planks if something catches on it.

The manufacturer came out and said that they didn't think it was a significant problem, although they admitted that some planks seemed outside of their tolerance, that the problem would lessen over the next year of acclimation (even though the floors had about 2 months to acclimate in the unit), and suggested gently that it might be an installation problem. They said if it bothered us we could screen and recoat and they would provide the materials for the recoat.

I have no idea if I'm going to get anyone to actually help compensate for this, but I'm unsure what to do here. I can't see how screening and recoating would make any significant difference for overwood. Refinishing is expensive and time consuming and takes away some of the wear layer (and also takes away some of the extra hard factory finished coating), even if the wear layer on these floors is thicker than average at 3/16". Some people I've talked to said the only solution is to tear it all out and start again, that the floor installer should have stopped when they thought there was a problem and sorted out what the issue was before continuing.

It is normal to have over wood on any pre-finished floor. That is why most have bevels, so you don't get a splinter. If the manufacturer has seen the floor and stands behind it you will have no recourse with the company.
If you like the color just use it. The finish ought to hold up for years. Is there a finish warrantee? some are for one year and others are for a long time. Eventually the "high" spots will show wear first. Another coat of finish later will help protect it from wear through.

Absolutely.

Once the micro bevels are sanded out what's left on the veneer?

Watch this video to get a better understanding.

https://www.youtube.com/watch?v=ltcU7CNkq-I

Carlisle does brag about their milling.
I'd ask for more than some finish and sand paper. Ask for replacement on their dime.

FWIW Istallers do not know what manufacturers tolerances are.

Carlisle had some good stuff years back until it was sold by the original owners. Unfortunately it became more of a marketing company with lower quality and higher prices.

I've had a handful of jobs where we matched some of their colors.