You are in a cost vs time situation. 65 is going to cost 10-15% more fuel than 55. 75 will cost you almost 35% more fuel than 55.
Most people average 50 mph with stops included on a towing day. 400 miles is a long day, 500 miles is a really long, tiring day. 600 miles is exhausting and may require resting up the next day.
From San Antonio - Van Horn TX is about the maximum drive. Fort Stockton is better. No real good places to stop other than Balmorhea along I-10 in west Texas.
With that trailer you will likely want to take the bypass around downtown which may be slower, but will definitely be easier.
Second night stop would be Lordsburg, NM or Benson, AZ, might want to push into Tucson.
EDIT - I thought you were going to LA.
We did San Diego (Jamal) to Bridgeport northwest to Fort Worth in January with two night stops - Benson AZ and Pecos, TX. I was exhausted upon arrival. (We wanted to be there for my son's surgery. I slept more than he did the next couple days).
You are going to need to learn to check your trailer tires for high temps which would indicate low pressure or brake issues. ST trailer tires are not rated for speeds over 60 mph though we all do so at some times.
Another factor to consider is weather. If I have a "must be there" date, I always allow one or two extra days for possible weather delays. High winds can be an issue almost anywhere along that route, along with the possibility of thunder storms.