The 127H-1 has a bigger magnet, a different dustcap, and a heavier cone than the 125A or 127H. Definitely won't work the same.
In this case, the 127H-1 is the BETTER driver. Better motor, slightly less distortion. Leave it the way it's supposed to be.
IMPORTANT NOTE: Make SURE that whoever does your 127H-1s uses the CORRECT surround. There are surrounds ESPECIALLY made for the 125A, 127H and 127H-1 (despite the other differences, they DO share the same surround). The generic surrounds most places carry are TOO STIFF and will upset the low bass to midbass balance (ie, the speaker will have too little low bass and be boomy in the midbass). The correct aftermarket surrounds (at least the ones that MOST shops will have available to them) will have a slightly REDDISH tint, and will be VERY COMPLIANT (ie, very flexible, or "soft", in industry parlance). If your local shop says they can't get the specific 125A/127H surrounds, then contact me... I have PLENTY of them here, and can send you some of the RIGHT ones...
Regards,
Gordon.