Just out of curiosity, at what point should I start attempting to get those days off. I would imagine that swapping days with someone else would be easiest way for a low seniority guy to get a streak of 5 days or so. No big deal if it doesn't happen, but what the heck, I'll give it a shot.

Good attitude. It typically doesn't hurt to ask. Your best bet is to try to swing a block of days while scheduling your IOE. Some guys go quick, some wait awhile, so why not ask if you can be one of the waiting guys? Just be up front about it with M, the IOE scheduler. Maybe she'll be able to help, maybe not. I'm sure she is very very busy.

Once you're done with IOE and put online, your chances go down, unless you get lucky and bid a green line with better than 13 days off. It can be tricky to swap enough days when you and all of your friends all have just 11 days off!