For clarification, this species is A. hybridus. I've never seen it referred to as brown-handed spider monkey, I think it's generally called brown spider monkey or variegated spider monkey. The three species known to be held in the US as far as I'm aware are A. geoffroyi, A. fusciceps, and A. hybridus (there are very few left of this one however). There may be hybrids of other species, and the subspecies situation is complicated by the unresolved taxonomy and many unidentified individuals.
not A. fusciceps fusciceps, but A. fusciceps rufiventris. Brown-headed is used for this taxon, but it is in fact the name of the nominal subspecies, better to use Colombian Black Spider Monkey (which has a black head!) Philadelphia no longer keeps hybridus, not sure if any is left in the US.
Given that its debatable whether they are their own species, are there more zoos that carry Ateles fusciceps but advertise them as A. geoffroyi? Many zoos have "all black" Geoffroy's spider monkeys that look more like fusciceps does. Most "true" Geoffroys seem to have white bellies and more often then not are also brown. If the all black Geoffroys are indeed fusciceps, this would certainly boost the number of zoos with the latter.
It’s worth noting that Tanganyika Wildlife Park recently obtained a pair of Red-Faced Spider Monkeys, making them the only holder of this species in the country.