We would use vai and vao if you wanted the 11-limit implications, but the pai/pao notation only really translates 5-limit information. If you wanted to mix and match you could, as the two commas are of course equal here, while tai/tao disappears. However, while using both vai/vao and pai/pao pairs you could easily translate information across tunings, they mean the same thing in 22edo, so you only need one pair. The pair recommended on the Sagittal article is pai/pao, which will link 22 with other common EDOs like 34, 41, 53, 72.
If you want to be able to translate your intervals and chords to ANY tuning, I'd recommend notating in JI, so that a 4:5:6:7:9:11 on C would be notated C-E
, however the effective temperaments in play will change how some intervals and chords relate to each other.