I don't think there's a thing you could have done. BHM was listed
as the approach facility, I would have waited until transferred to BHM
to ask for the approach I wanted. If it was less than 30 nm out, might
query ATC facility I'm talking to "N123 requests RNAV 33 at EET", which
would probably get you a "I'll be handing you off in a minute, ask them"
response most of the time but would have helped this time.

A while back on these newsgroups, I was asking how to get a chart of
the airspace different facilities control. I was told I might as well
ask for the moon, more likely.

My instructor told me that the airspace that a particular facility controls
can change on a day to day basis, depending on which runways are in use at
the various airports in the affected areas. Airspaces tend to overlap, so
when the winds shift around, causing different runways to be in use, the
tracons will adjust their airspace boundaries. Or something like that.

Bottom line is exactly what was said... use the charts as a guide, not as an
absolute rule for who owns the airspace on a given day. And ignore ATC when
they "complain" that you should be able to read their minds.