I was also thinking about this, and I think one good program would be the masters in math program at NYU. The deadline for applications was very late, somewhere around May or June. It is also a very good place to study math, and it seems like there is some flexibility in course choice. Of course, you might need a bit of math to get accepted. I think Brookings and the CEA both do their hiring late. The Chicago fed also recently contacted me for an interview, so they may still be hiring too. As for the question of whether it is easy to take classes part-time as an RA, I think so. When I interviewed for a few RA positions they said this was common, and some even offer to pay.