. . . the one that gives you the right chainline!

You ran out of room with the spindle replacement because the spindle you were substituting has a smaller distance between the bearing tracks than the one that originally worked with the cups you have. TA and Stronglight have quite a wide track; even more than lots of Italian spindles -- look at Sutherland's and you'll see what I mean. Bear in mind that a cartridge bearing BB will have JIS tapers -- a bit chunkier ends than a TA -- so you may need a slightly shorter SER (shell-to-end, right; Sutherland's parlance) than the diagram above suggests. If you can, buy from someplace that will let you return; or have the shop do it.