@tpcraigs they send out rosters roughly five times: something like, March 1st, March 15th, April 5th, May 2nd, June 3rd.
You are definitely running out of time.
Whatever your first choice is already got notified (unless you are undecided). You can switch now to a new one and they will see you on the April roster. The May 1 might be too late for some places. I don’t remember which one NM uses to send out official college scholarship offers, but once you get that offer, you can’t switch and get a different one.
If you want the definitive word, though, call NMSC. They are incredibly helpful.