Just to be clear, in your original post you said you tend to use index middle pinky where others are using index middle ring, correct? And this is in the context of whole step followed by half step (i.e. 5 7 8 on the E string like @Pepepicks66 mentioned). I just want to make sure there wasn’t a typo Because you also mentioned for the whole step / whole step pattern (i.e. 5 7 9) you do it Paul’s way (index ring pinky). I’d absolutely expect a speed limit using index ring pinky.
Just like a tremolo is a test of how fast we can pick, a 3 finger ascending (or descending) roll is the faster we’ll be able to move our fretting hand. If you try the following, all hammer ons on one string repeatedly:
(With fingers index middle ring)
|-5-6-7-5-6-7-5-6-7-5-6-7-etc-|
OR
(with fingers index middle pinky)
|-5-6-8-5-6-8-5-6-8-5-6-8-etc-|
The idea in each case is to release (i.e. empty tension) the index as the middle frets. Release the middle as the (ring or pinky) frets. Release the (ring or pinky) as the cycle starts over again. This always gives each finger maximal time to recover and play again.
There are several things that can make this feel easier/harder. The position of your fretting hand and wrist (such as how parallel to the frets your fingers are, how bent/straight your wrist is), which string you are playing on, how wide the stretch is, whether your fingers are arched/straight in relation to what your personal hand at rest looks like. I’d say to try a variety of things until you find which parameters allow maximum speed. Once you establish a baseline, try it with the ‘other group’ of fingers and try to match the speed you achieved. Ideally index middle ring and index middle pinky will be equivalent. In most people, index ring pinky won’t have the stamina.
Lastly, I mentioned all hammers and ascending. But all hammers descending should have the same speed potential.
Good luck!