Hello Peter !
Sorry for my late answer, I am away from everything at the moment, and I am
reduced to answer your message with a mobile phone :-)
I believe that this thing is slow because we did not inform the LP data
structure (which we do not encode ourselves in Sage) or the problem's size.
While analyzing why a program becomes unexpectedly slow (despite moderate
memory usage and no swapping), I found out that the time consumption of the
method add_constraint slows down if there are already many constraints.
The following simple (and silly) program displays this:
P =