Even the ENT bible suggests that he should have been a lieutenant. It suggested Trip was to be one too, but we saw that in the flashback to before Enterprise's launch in "First Flight". We never saw Mayweather as a lieutenant, even in an alternate reality scenario.
Had they cast someone a few years older as Travis, he likely would have been a Lt.
My head canon is that Riker's holosimulation was either historically inaccurate (the way a movie set in 1810 might feature details from 1805 or 1815) or deliberately tweaked to include historically significant characters. Might've had a few outdated images, which is why no one looked any older despite six years having passed.
By 2161, Hoshi was certainly a lieutenant, while Mayweather should have been newly promoted to commander and assigned as first officer on one of the newer NX's. Phlox had probably returned to his practice and family on Denobula, T'Pol was commanding her own ship, maybe the same one Mayweather was on (that's why her romance with Trip ended; long distance relationships rarely do well). Reed was... I don't know. Maybe a commander working in a shipyard, refining ship armaments (and doing the occasional favor for his pals in Section 31). Trip had probably declined promotion so that he could stay with Archer, hence him being present for the events being reenacted.