  We consider the large-time dynamics of one-dimensional processes involving
adsorption and desorption of extended hard-core particles (dimers,
trimers,\,$\cdots,k$-mers), while interacting through their constituent
monomers. Desorption can occur whether or not these latter adsorbed together,
which leads to reconstitution of $k$-mers and the appearance of sectors of
motion with nonlocal conservation laws for $k \ge 3$. Dynamic exponents of the
sector including the empty chain are evaluated by finite-size scaling analyses
of the relaxation times embodied in the spectral gaps of evolution operators.
For attractive interactions it is found that in the low-temperature limit such
time scales converge to those of the Glauber dynamics, thus suggesting a
diffusive universality class for $k \ge 2$. This is also tested by simulated
quenches down to $T=0$ where a common scaling function emerges. By contrast,
under repulsive interactions the low-temperature dynamics is characterized by
metastable states which decay subdiffusively to a highly degenerate and
partially jammed phase.
