Yes, the Baikals have a jack screw in about the same position, which serves the same function.The challenge will be in getting the amount of tension at the midpoint right - a little bit of pressure makes a noticeable difference - and then fixing it in some way so it doesn't move.
The other way you might do it, though I haven't tried it myself, is shimming the band at the muzzles to bring the muzzles slightly closer together. Once you have the two barrels shooting to more or less the same POI you would re-zero the sights.
The problem with shimming the bands, which usually requires relieving them to allow shimming, often changes windage a bit, or a lot if not done with utmost care.
As you correctly state, a little pressure or movement can make big POI movement. Also, IMO, shimming at the front band can really adversely affect general accuracy/widen groups, especially as barrels heat up.
It's an interesting project that I wouldn't like to undertake.