A Master's in Engineering makes you more competitive at the board, but it is not a requirement. A letter of recommendation from a TPS graduate (or 2) probably has more weight for pilots quite honestly. Plus you get a Master's of Science in Flight Test Engineering for going through the course. The only thing a Master's in Engineering opens up for you is if you want to get selected for the TPS PhD program after TPS.
In my class about 1/2 of the pilots had an Engineering Masters, 1/3 had non-Engineering Master's degrees (ERAU, MBA, etc.), and some had no Master's degree prior to TPS.
Plus there is an AFIT TPS option. Take the GRE and get a Letter of Academic Eligibility from AFIT for their Aero or Electrical Engineering Masters program then apply for TPS with the AFIT box checked on the application.
As far as how to get a letter of recommendation from a TPS grad. Find out who the TPS grads are that are working DT on your airframe, get in touch with them, and convince them you are they guy or gal they want to work with. Figuring out a permissive TDY out to Edwards or just straight up taking leave to go there on your own to check it out sends a pretty strong message. Plus you will realize where you are signing up to live for possibly the bulk of your active duty career going forward. The flight line is like an airshow everyday especially when TPS has qual eval aircraft in town, but it is a very remote place to live for people that like urban amenities...like a drive through Starbucks, fully stocked liquor store, or gym that isn't as old (or older) than all the bombers on the flight line.
If you want to do an online MS go for it. It certainly won't hurt you. One of my classmates did the CSU program that was mentioned, and I know at least 3 TPS grads that did the MS Program from the University of Alabama.
https://catalog.ua.edu/graduate/engineering/aerospace-mechanics/ms/