Can my husband claim one house as his primary residence, and can I
claim another as mine...so that we can EACH take advantage of
Florida's reduced homestead personal property taxes on EACH property? 
(We would substantiate our residencies with driver's licenses, utility
bills, and voter registrations.) Our intent is to use our existing
home as MY residence, while he lives in a new home for at least two
years.  We can't decide now if we want to permanently live in the new
house...and we might sell it at the end of two years, and go back to
our original home....or sell that one too.  Can we then use the
$250,000 tax exclusion on each home. Bottom line is we also want this
to be a legal and legitimate method to avoid any increase in the
property tax (from lack of homestead reduction) on the original home.

husband & wife are not required by any law to live at the same address.
so, my suggested answer is Yes, you can.

$250,000 tax exclusions is different.
if you jointly owned the home, each of you will have a half of gain
and could claim up to $250,000 tax exclusions.
If you are selling second house in less then 2 years exclusion
couldn't be claimed by any of you.
If you and your husband owned separate houses and not live in
community property state (Florida is not), then each of you will have
separate gain.

I would be more than happy to give any clarification