I turned a piece of 5/16" diameter 12L14 steel down to 0.2755" in 0.005" increments using a carbide insert cutter,
Five thou on the diameter, or 5 thou on the radius? Either way, I do not know the inserts you're using, or where there limits lie, but small cuts take a sharp insert, otherwise they start to generate excessive toolpressure.
then down to .02750" using 400, 600, 1299 and 2500 grit oiled sandpaper.
Were you aware of and paying attention to this taper as you were sandpapering? Or was the taper discovered afterwards.
Hand sanding can easily do that, ESPECIALLY on a short piece like that. It's hard to get as much pressure and contact time on the piece up close to a shoulder, and easier out towards an end. It's VERY easy to do this. I would say that unless you mic'ed both ends after the cut, and throughout the cleanup process, you should probably not worry too much about anything else, as there's so many "could have been" items that you'd just be pinning a tail on the donkey at this point.
The material projection from the ER32 chuck was 0.6875", using the L/D rule of thumb I figured I'd be good for up to 0.825", 3 times the finish diameter.
You should be good at that size, within reason, depending on what you're doing. Don't forget that there is NO RULE about how much can or can not stick out. It's not a hard number. It depends on the material, the diameters, the tool pressure, the cut direction, all kinds of things. It's a good "rule of thumb", but it's not a law of physics. But like I say, this probably shouldda been good in that regard
From the chuck end of the cut, my DTI indicates a near-perfect axial zero reading up to about 0.4602", then it falls off rapidly, and linearly to the TS end of the piece. The taper at the end is radially 0.0015" less than the chuck end.
That's "probably" not deflection. Deflection from tool pressure would make the tailstock end fatter. It's possible that you got right into the exact cut that makes your tool want to "dig in" and pull the work some... It' can happen as you cross the boundry from a cut that's deep enough for the tool you're using, to a cut that isn't deep enough for the tool you're using.
My first thought is this must be due to workpiece deflection but since my L/D ratio is "in-spec", I wonder if there's something else going on?
I'm still leaning on the sanding operation...
I've already corrected the lathe for bed twist and don't believe it would cause such a rapid taper at one end of the work while allowing roundness further back.
Also wonder if maybe this might be caused by a wear spot in the ways; either low or high?
It's too localized for that. Even if you had a ten thousandths gouge in the lathe bed, if the gouge was small enough to do this, the saddle would bridge it. Or if it was twist, it wouldn't be so localized.
I may try using a dead or live center on a piece to see if it's deflection-related, thought I'd ask here first.
If you're questioning the accuracy of the machine, the tailstock should be out of the equation at this point. I wouldn't go there just yet.
If that were me I'd cut some test pieces to see what happens. You're taking of 37 thousandths, 18 on a side... I use high speed steel tools mostly, but if you can picture this, maybe you have an insert that can work?
I'd have the tool cutting edge exactly perpendicular to the lathe centerline, and split the cut. 9 on the first pass (18 on diameter), and then the same thing on the second pass, adjusted for any descrepancy in the first cut, to land on the final dimension. If I had to make six of them, I'd do a test piece or three, and figure out the number to dial that all into one cut.
Regardless of how you get there, the dimension of the WHOLE THING needs to be checked on the cut, NOT on the sanded, finished product. At that size it's very, very difficult to maintain (or correct) dimensions unless you measure OFTEN and adjust the pressure/placement to accomodate.