I'm curious about the "All proficiency flights will be conducted in
airspace within an operational radius of 300 nautical miles from the
airport where the aircraft is based" part.

What defines the aircraft's base of operations?

Am I limited to one BofO per year? If not, then how many? Perhaps if I
plan on doing a 500 mile straight-out, I can declare a new BofO for
the second half of the flight?

I'm imagining a 21st century flight recorder that wirelessly emails
the FSDO a new BofO declaration when a GPS fix approaches the 300 mile
limit from the last one ...