I've seen several specs for the TA 373 spindle between 117-120 mm in length, IIRC, and 122-125.5 for the 374, IIRC.

I rode a lot of miles with a Sakae Ringyo axle that put the chainwheels too close to the BB, so the chainline centered on the 2nd largest cog in my U-6 freewheel instead of between the 3rd and 4th cogs. I used the freewheel until a few years ago (on my one bike) without any problems, other than aesthetic, on the bike or myself.

But I don't know what BB and spindle go with the TA Pro that came on the Competition. My advice is to try it, ride it if it's ridable, and shoot an email to Specialites TA in France to get their input. I am OCD enough to want the chainline right, but with a 120 or 125 mm hub, cross chaining is much less a problem than with a 130 or 135 mm hub, so the chainline is less critical, in my non-engineer's opinion.

Sure, I'd want a pretty chainline, but I'd ride first and then get the chainline correct, but an engineer may correct me - but, please, only if it really is a problem in the short term.