I would imagine that there are two simultaneous metabolic systems operating side-by-side. The first is the standard human metabolic system, where people grow older, stronger, or weaker on a semi-determined time-scale (telomeric degeneration, etc.). That this operates is somewhat of a truism, since Logan has aged (and will continue to age, if you take 'Old Man Logan' as a true continuity). The second is his mutant metabolism, that repairs the damage he suffers. This second system is only overlaid on the first, however. It does not override it, as you can see from his ability to form new memories, and his aging in Old Man Logan.
As to the state to which it is repaired to (and to support the bi-metabolic hypothesis), there has to be some genetic marker guiding the repair (i.e. the mutant metabolic process is not sentient, but a reactive part of his physical person). That marker would then act like a 'snapshot' as you said, to guide the repair - but there is no reason to assume that it truly interferes with the standard metabolic process (or else he could not, say, form new memories). Indeed, because Logan ages, we know that it does not ultimately interfere with the process on a long enough time-scale (yes, I know he is very old, but he is aging). The mutant regeneration is not static, it is simply that the way in which it operates is so rapid that it interferes with normal degeneration, and thus slows the aging process to a near standstill, and would do so likewise for growth (muscular, in our case in point). Logan would have to work out so hard and so long that it might not be practically possible for him to put on more muscle mass, but per the rules under which his regeneration operates, he should still be able to, albeit at the same snails pace with which he is aging. It would follow then, as a fun consequence, that if you took his healing factor he would not 'turn to dust' like he would is there was a magical preservation that was later taken, but rather simply age at an appropriate rate relative to his cellular development.
TL/DR: His muscular breakdown would be recognized by his body as part of a normal metabolic process, but the repair signal, modified by his regenerative capacity, would be so minor as to significantly retard muscular growth (via muscular destruction). Likewise, since he will continue to age into the future, there is proof that an overarching, standard metabolic/genetic system determines the ultimate path of his development, simply modified by an ability to heal that slows every aspect of that development.