Yep, NRSA can go into Economy Plus with no rule breaking, assuming it's available (duh!) and the gate agent is nice enough to think about it (sometimes they go with the default seat assignment, which may or may not be E+). If you ask really nicely, they may reassign you if you don't get it the first time.

Where were you getting your load information? Seat map on united.com? If so, don't. Those are not reliable, as they leave seats open on there when it could simply be a matter of a passenger having a flight booked without a seat assignment. An hour or two before departure those are a little more reliable, though.

I can tell you that UA1098 and UA1055 on your outbound look great, the other two are a little more iffy (but not impossible). Return flights those days are booked evenly AT BEST.