The only way I could figure out how to get different output for
monolithic and section-based versions was to do this rather odd hack,
which uses tex4ht.usr to conditionally insert specific bootstrap HTML
for the mention that will allow proper formatting.
tex4ht supports "overlib" for footnote popups. The hack is pretty
straightforward; it dumps a Javascript area into a .js file that can
then be used by overlib to popup stuff.
This hack is to use that output to make the same thing work with jQuery
UI's tooltip widget.
Note that we run with overlib support first, then *without* it in the
Makefile setup. This is to force the needed .js file to be generated,
but make sure the HTML doesn't try to load overlib (which is default).
(This should be adapted as a patch to upstream tex4ht ultimately.)
Also included herein are improvements to the Makefile to build the HTML
output.