I don't have my rifle barrels with me.

But I do NOT believe any were "free floating" at the muuzle.

I assume that "saddle" below should be attached to the upper barrel. And the saddles wedge below is what is moved sideways to influence the regulation. The rear wedges on the barrels influence height of bullet impact. So the muzzle ones affect lateral regulation. I never have had to fiddle with the front muzzle wedges.

I don't imagine resoldering the barrel at the muzzle is difficult or costly.

Someone more knowledgeable might chime in.