Having a bunch of random bottom bracket parts, I would like to make use of these on builds since they can be rebuilt rather than disposable cartridge bearings and I just like their classic look. However I haven't had much luck matching the spindles and cups together and am to the point of throwing in the towel. The problem is when adjusting for the sweet spot, tightening the adjustable cup and immediately after the crank loses play, the spindle binds up. Even though the parts are all made for 1/4" bearings, this would seems to indicate the race diameters can vary and even the slightest amount would probably cause this effect. Are there any tips for finding matching spindles and cups, none of which are from the same set? In other words, has anyone had luck in the interchangeability of these parts?

assembling "loose ball"? you probably have one too many balls in the assembly.

install caged bearings... see if it works.

there is apparent room for 11 balls, but you should only install ten, if assembling loose, no cage

Assuming these are all "British standard"-
Since the spindle/axle bearing races are machined to a "standard", the cups have to be machined to a matching "standard".
Your adjustment has to be down to a degree or 2 of "rotation". Not very much between "perfect" and not.
Do you have the tool to keep the adjustable cup from "creeping" slightly when tightening the lock nut?

For TA Axix you can buy individual pieces. Those pieces are interchangeable with World Class, not in production but hovering over Ebay persistently and cheaper there, than new TA in titanium version. In addition couple of other brands can be interchanged with these with some success, such as not completely sealing the bearings, but working.

Even among Campagnolo there have been a varieti of spindle specs . wider , italian/70 ; BSC 68 , thick with rifling to expel grit without a seal,
or thin cups, that did not employ that feature..