If the old pump had some issues keeping proper pressure for some reason then maybe it is the tune, but I'm fairly sure the old pump would have problems keeping pressure once you got on the gas even more so than low down.
TBH sounds like air bubbles or something like that, whereby lowdown the restriction is noticeable, but up high not so much. Lastly, what happens if you turn on/off music/AC/headlights, that should narrow down if it is electrical supply issue (possible if the alternator is on the way out).
Ultimately, just pay your mechanic $50 to diagnose it properly before something breaks