Charles Wahl

I don't see how the above makes sense at all. OP is trying to adapt a (supposedly) "track" set of crank arms to use as a double. The difference between a drive-side crank intended for a single chainring and a double is going to be (probably) the lack of lands for the inner ring on the backsides of the arms (no big deal), not the dimensional relationship between outer ring and the spindle end. The only reason one would use a TA 314 spindle would be to achieve having a single chainring (mounted outside the arms) situated closer to the centerline of the bike than the outer ring of a double. IF OP were looking for a replacement TA spindle to use, then the one marked 344 (see table above) would be the one to shoot for. But he's not; he wants to mount the arms on a cartridge bearing BB assembly. Were I doing that, I would look for a JIS unit (as Sutherland's suggests) with a slightly shorter spindle length than the proper TA spindle for the BB configuration that has the correct number of chainrings. BTW, I have at least 3 TA spindles marked 344, and they actually vary in length a bit: 114.5, 115 and 116.5, even though Sutherland's says 116.5 is the nominal length. I certainly wouldn't go for the 121 mm unit that OP has bought -- something more like 114 or 115 mm; unless he spends more than 75% of the time on the smaller chainring. I also wouldn't buy a used cartridge BB unit on eBay, but that's just me -- why take the risk for a bit of savings?

BTW, my impression is that one can swap TA and Stronglight arms and spindles that are nominally the same size with a fair degree of confidence that they'll work out OK -- apart from the differences between parts due to manufacturing tolerance (which, in my experience are greater for TA and Stronglight than for, say Sugino, which seem to me to have tighter tolerance) they're very close to each other in terms of taper and length, distance between nominal bearing running surfaces (fit of spindle to cups), etc. And, based on used examples that I have, they are extremely durable parts, compared to Campagnolo or Shimano; comparable to Sugino. But, if OP wants cartridge (no problem, I like those too), then all this is immaterial.