GPS approaches with Center

How many here have flown GPS approaches with Center as the approach control?
I'd be interested to hear your experiences.

I needed to fly one yesterday to get into Greenville, AL and the ZTL
controller sounded really befuddled about quite how to handle it. Because of
another recent experience, I told her 35 miles out just what I wanted to do,
including the name of the IAF I wanted to use. Her response was to clear me
down to 3,000', but nothing more. After about 10 miles of silence, I asked
her to clear me direct to the IAF and told her the heading I would need. She
said:

"Cessna '87D, cleared...ah...for what you requested. Maintain at or above
two thousand one hundred until established on the approach, cleared approach
to Greenville, report canceling...etc."

Now, the minimum altitude on that segment of the approach is 3,000'. Does
her altitude restriction of 2,100' mean she had no way of knowing that, and
could only use her MVA? After she cleared me, she came back a couple of
minutes later and asked me to spell the IAF waypoint again.

It seems that the Centers I talk to always fumble a bit when I ask for one
of these approaches. What's the problem?

The fun part of this was getting to say "UGMUF" several times on the radio.
--
Dan
C172RG at BFM