There is a collection of references on strongly interacting dark matter candidates at
http://en.wikipedia.org/wiki/Strongly_interacting_massive_particle, SIMPs. In these works, it is not necessarily the case that the self-interaction is the strong interaction of QCD, but some references, in particular
Wandelt et al also consider that possibility.
An important result is contained in the paper by
Mack et al. Previously exclusion limits on SIMPs had been derived from astrophysical limits and underground detector non-observation, leaving a window in the space of cross-section vs. mass plot (see in particular fig. 2 of
Zaharijas and Farrar.) Mack et al consider the case where the SIMP is its own antiparticle and find that annihilation processes would lead to excessive heating of the Earth.
A further constraint, coming from gamma ray production via cosmic ray proton-dark matter interactions, is considered by
Mack and Manohar, where it is argued that a huge window is closed. This analysis does not seem to rely on assuming any properties of DM particle and antiparticle, and would presumably apply even in the case where there was a large matter-antimatter asymmetry in the dark matter sector.
In any case, this seems to be an interesting topic that would be worthwhile to understand even if the end result is negative.