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Don't ever believe that shifting before red line is helping in improving acceleration stats. When it would, BMW would be total crap in setting up a transmission line. Really, I don't believe they have sunk this deep yet, this is pure basic stuff that even LADA could do perfectly fine ages ago!? BMW is still taking driveline set-up sufficiently seriously these days.
On the other hand, you state that torque is limited in first gears... Where did you get this? I understand that none premiums do this to limit strain on the transmission or can't cope with it in their FWD set-up, but the 125d is neither of both. So I'd expect full access to torque as from 1st gear...
Have you disabled DTSC to allow some spin? At this level, figures are made with controlled burning rubber. You'd have to rev to ~2500rpm, when you floor throttle, the rpm settles on this automatically. Also have totally disengaged the DSTC (hold the button a bit longer until it indicates on the dash it's out).
Then you release clutch almost instantly while keeping the accelerator to the floor. Go up until just before limiter in both first gears. When the spin is feeling too excessive, go a bit softer on the accelerator to gain more grip earlier in the process while trying to sustain the controlled spin as long as possible.
On the other hand, acceleration from stand still is too much dominated by the stand still grip and inertion and doesn't reflect vehicle dynamics sufficiently. It would for low torqued cars, but the 125d is on the other side...
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