I got around to measuring the stiffness of the toolpost assembly, both crosswise (perpendicular to the bedways) and longitudinal (parallel to the bedways.
The setup consists of a 3/4" OD 1018 bar held (with a sleeve) in a BXA-4D boring bar holder, and a 1.5" by 0.5" aluminum bar clamped to the top of the BXA-4D. The lathe is not running. The round steel bar is used to apply torque, while the rectangular aluminum bar is used to move a dial indicator. Two bars are used so that bending of the steel bar will not contaminate measurement of angular deflection of the toolpost.
Crosswise: 621 foot-pounds of torque to cause one degree of deflection of the BXA toolpost. (Torgue: 5 Kg at 32" from the 5/8-20 bolt. Deflection: 0.005" at 6.75" from the bolt.) The torque is applied in the same direction as from normal cutting forces, with tool advancing from the front and the workpiece rotating in the normal direction (top approaching).
Lengthwise: 516 foot-pounds of torque to cause one degree of deflection. (Torgue: 5 Kg at 32.75" from the 5/8-20 bolt. Deflection:0.013" at 13" from the bolt.)
So, crosswise is 20% stiffer than lengthwise, which isn't much - call it equal.
While I was measuring crosswise a second time, I noticed that if I pressed down on the 3/4" bar hard enough, the carriage would lift off the front bedway rail with a definite clunk sound. This happened when the deflection exceeded 0.015" at 10.75" from bolt. The deflection due to the 5Kg weight is 0.0055" at 10.75", so it takes about (3*5)(2.2)= 33 pounds at 30" (83 foot-pounds) to cause the carriage to lift off the rail. The tilting of the toolpost is both audible and visible.
Pulling up on the bar did not cause the carriage to lift off the back rail, probably because I had already cleaned and tightened the back hold-down clamps.
Anyway, this is another reason I was seeing visible deflection while pushing the toolpost around, even with tight gibs, and this motion would cause some self-feeding on heavy cuts.
So, I took the two front carriage hold-down clamps apart, cleaned them, and reinstalled with far fewer shims. The left front hold-down clamp needed no shims at all, losing 0.0085" worth of shims. The right front hold-down clamp was also cleaned and reinstalled, but needed two 0.0015" shims. The hold-down clamps are bolted to the underside of the carriage, the bolts screwing into a blinded threaded hole that is open only on the bottom.
There were four brass shims per front hold-down clamp, two 0.002", and two 0.003" (nominal), and it appears that the original shims were still there, with no allowance for wear having been made over the years.
Oddly, the right front threaded hole was full of chips and grit. I imagine that the lathe was run with this missing for some time, or it's hard to see how chips and grit could get up into this well-protected hole. Anyway, cleaned it out.
Now, one cannot get the carriage to lift off the rails with any reasonable level of force, which is to say that the carriage runs into the front hold-down clamps before the oil film between carriage and ways lets go and sucks air in.
The rear hold-down clamps were cleaned and tightened some time ago, so now all four hold-down clamps have been done.
While I was at it, I cleaned and greased the carriage lock bolt and mating carriage clamp. Again, lots of black goop and grit was washed out of the assembly, and it now works far more smoothly.