Getting 68 sliders is the simplest solution except very difficult to find.
Afaik, they're one-year-only?
'68-on, Meriden supplied TLS (and full-width SLS for the 250's) complete with spindles. Pre-'69, Triumph fork yokes placed the leg centres only 6-1/2" apart, 1/4" less than BSA's 6-3/4"; '69-on, Triumph yokes were changed to place the fork leg centres the same 6-3/4" apart as BSA.
So the 37-1641 spindle is 1/4" shorter than the '69 37-2057 and '70-on 37-3582. So afaik spindle clamps just on '68 BSA TLS (and 250 SLS) sliders are 1/4" closer together between two fork legs.
Also if you swap between pre-'69 and '69-on spindles, be sure to keep the brake plate nut on the spindle - pre-'69 is 20 tpi British Standard Cycle, '69-on are 20 tpi UNEF; at least one internal thread (nut) doesn't fit on the other external (spindle) thread.
For a different reason - the cable abutment position - the '68 TLS brake plate is also one-year-only. "69-70" brake plates are "more plentiful" than '68 but only up to a point - while Triumph continued to fit them to '71-'74 T100 500's, because Triumph did evolution not revolution, the TLS is backward-compatible before '68, and Triumph owners have been fitting the better brake to earlier twins for many years.
have a full front end from a 69 Triumph. I read somewhere that a company makes bearings and shims to convert to Triumph front.
Both use twenty 1/4"-o.d. balls top and bottom, so they cannot be significantly different? Does your "full front end from a 69 Triumph" include bearing cups 'n' cones? If not, they're easily available; acquire them, measure them and compare with BSA cups 'n' cones?