The answer is specific to individual circumstances, I trained and taught at both 61 and 141 schools but that was all before R-ATP was a thing.

From observations over the years, I would not pursue a specific path solely BECAUSE of R-ATP eligibility... in the grand scheme the 500 or 250 hour shortcut isn't necessarily worth jumping through the hoops (and 141 university programs obviously take longer).

I'd pursue the fastest path that works best for your situation and finances. If R-ATP lines up with that, possibly due to GI Bill requirements, then great.

For planning purposes, with a tiny bit of luck and some hustle you can easily get 500 hours in six months as a CFI. Assuming that six months isn't over the winter in snow country.

Also are you doing a full 4-year degree? Normally that's highly recommended for airline-bound folks but at this moment there is still some good retirement movement at the big three through the end of the decade. Might be worth just knocking out ratings and getting on with a regional to build time... you might be able to get hired by a major without a degree, if not you could chip away at it via distance learning while building time at the regionals.