Sink holes in drainage area
Having had some time to do some digging (hahaha), I have as close to an answer as I believe is possible.

Small update just because: one of the smaller sinkholes has dangerously grown, in a way that I wouldn't believe if I didn't see it.  It has widened slightly to about 45-60 cm, but grew substantially deeper.  With a tape measure I clocked it in at 3.3m.  No joke.  It's pretty much a death trap to small animals or children.  I do not take my children back there anymore nor does anyone else seem to play there, fortunately.

Onto answering my question.  This is Florida, the land of sinkholes, and it seems that the assumption made by all parties involved is that this is an actual sink hole, and not some obscure side effect of the drainage area.  After querying my HOA I learned that the area is owned/managed by the local county government.  It doesn't sound like they bother doing geological studies (because sink holes are so common around here), but instead just fill sink holes in as they appear to avoid liability.  They are actually aware of the larger hole and put it on an "official" sink hole map (which will probably have a minor effect on my insurance rates).  They will also fill it in.  However, they are being quite slow about actually fixing it (which is a surprise because of the potential liability issues).

From what I have read on various government sites, sink holes around here are assumed to be fairly independent, i.e. a sink hole within 50 feet of your home doesn't imply that your house is any more likely to experience damage from a sink hole than any other house in the general area.  However, since the organization responsible for filling the hole is not going to be performing a geological survey, nor are they likely to bother consulting professionals, a best guess is the best I'm going to get.