Reamer #5 was made. It only warped half as much as the previous two reamers, but it still warped noticeably. I marked the high spot on the runout and ground that high side off to make a "D" reamer. The theory was that the cutting edge would be straight, plus the D reamer should have enough flexibility to straighten itself out once inside the barrel.
The reamer pilot was a very snug fit in the bore -- the bore is 0.3478" and the pilot is 0.3475"+.
The chamber was reamed at 160 rpm, using plenty of cutting oil, pausing to clean chips frequently, and with the reamer allowed to "float" in an untightened drill chuck (the reamer was free to wobble inside the untightened drill chuck, the chuck was merely used for pushing the reamer forward).
The good news is that the D reamer cut with minimal effort and not much chattering.
The reamer measured 0.3795" at the neck and the finished chamber measured 0.3803" at the neck, so apparently the reamer was still warped enough to cut slightly oversize, though not enough to complain about.
The bad news is that the finish was rough, apparently due to chips getting wedged between the reamer and the chamber wall.
I test fired some full house loads and all cases failed to extract easily, and had to be tapped out with a cleaning rod. So I lightly honed the chamber with fine emery cloth, and tried again. Cases still failed to extract easily.
As near as I can tell the main problem is a chip gouge on the case neck, where the arrows are pointing in the photo. That shiny ring on the case is where the case expanded in the chip gouge, and then rubbed against the chamber as the case was extracted.
The gouge in question only extends 180 degrees around the chamber. I'm guessing it was caused by a chip getting momentarily wedged between the reamer and the chamber wall -- I can't think of any other explanation.
As you can imagine, I'm pretty frustrated.

I wanted this barrel to be a learning experience, and it has been a learning experience, the problem is that I'm learning everything the hard way.
Thoughts, Theories, and Plans for Next Time:
-- my brief experiences with D reamers suggests that they are more prone to chip gouging than conventional 5-fluted reamers. That's one reason I attempted to make 5-fluted reamers.
-- it may be that the reamer warping is not that serious a problem because 1) the reamer does not rotate and 2) I suspect that it tends to straighten itself out in the barrel, to some extent. Still, who wants to take a chance with a severely warped reamer ?
-- conventional wisdom holds that you should clean chips frequently, but I'm wondering if the gouges are happening when I reinsert the reamer into the chamber? I brush the chips off the reamer, and blow out the chamber with compressed air, but there's usually an errant chip or two still clinging to the reamer, and possibly an errant chip inside the chamber. Maybe I should defy conventional wisdom and continue reaming until the chamber is full depth, and only withdraw and reinsert to set the last few thousandths of headspace?
-- pros pump oil into the muzzle end of the barrel to flush chips out the breech end. No doubt that is the more superior method and perhaps would have eliminated my chip gouging problem, but it's a fairly big deal to set up so most hobby gunsmiths like me don't bother. Besides this barrel was too short for the muzzle to stick out of the lathe headstock, anyway.
-- I may have to break down and order a custom reamer, since my homemade 5-fluted reamers tend to warp excessively. I suspect the conventional 5-fluted reamers would have fewer problems with chip gouging.
-- because I'm itching to resume shooting projects, I may attempt to fill the gouge with JB weld and then re-ream after the JB hardens. It may not work, but I don't have much to lose by trying.
-- I've got a 6mm x 223 barrel TC project in the works, but I don't want to ream that chamber until I get the bugs sorted out of my chamber reaming methods. So the 6x223 is on hold until either 1) I get my homemade reamers figured out or 2) I buy a custom reamer.