They can't refuse you the use of the runway and taxiways. But can't
they refuse you road access to the airport, or the use of the apron for
assembly?

Hmmm...dunno about that one. But I just thought of a few more
things:

You can see if it's ok to land and takeoff from a taxiway.
Perhaps a little unlikely but an option.

You can arrange to land long. Min separation is 3000 ft between
aircraft, so really four SMALL aircraft can land at once on a
10,000 foot runway if the first one only uses 1000 feet.
If you can demonstrate you will land using only the last 1000
feet, that might alleviate problems. Also, landing right at the
high-speed point and immediately taxiing off would be
real cool (assuming taxiway lights are no problem).

Just a few more thoughts to throw into the
options...