I've enhanced your version of the patch to work with the following defines:

#define HAVE_TZNAME 1
#undef HAVE_TM_ZONE
#undef HAVE_STRUCT_TM_TM_ZONE
#undef HAVE_ALTZONE

It now uses struct_time in such an environment to provide the extra offset information used in the unixtime function rather than accessing tm_gmtoff. I suppose one could do that for all cases, in fact, since this is done independently of any mktime invocation.

The above defines probably represent the next most "sane" of environments after those which have tm_gmtoff. If one starts to remove other things, other more established tests seem to fail, too.
File Added: time-1-improved.diff