Spring Break is an extremely busy time of year at Big Bend NP.
I'm also finding Texas SP heavily booked for weekends months in advance.
I lost over $100 last year when the state of NM cancelled several paid state park reservations we had in June, July, Aug and Sep.
Don't know how far east you want to go, but there might be availability at some COE campgrounds near Canyon Lake, Proctor Lake, Hords Creek Lake.
Over the past 9 years, I found March to be busy and crowded in Texas as a lot of people put their rigs on the road for the first time of the year.
