I usually start at grit 50 in rotex mode like you did, then i do another pass in Random mode, then i switch to the ETS150/5 with grit 80-120-180-220.
I don't know the hardness of the wood you used, but on european beechwood i find it hard to conceive that you could go from P80 in rotex mode, directly to P120 in Random Orbit mode. It's possible that a brand new pad of 120 can get the P80 rotex swirls away. But i presume that would wear out the pad rapidly. I find it more economical to remove the rotex marks with the same grit in random mode first.
Depending on the finish i stop at 120 for acrylic, 180 for poly and 220 for oil. I once visited a factory that made oak and beechwood stairs with CNC mostly, they told me they never sand above 120, it's not necessary they told me, no matter the finish. And their finished stairs were impeccable to the eye and touch.
When using oil i was thought not to sand above 220 in order not to close the grain and make the wood impenetrable to any finish?
I use the festool surfix oil, sand to 220, apply oil, polish with rotex with rough polish pad, when dry sand with 320, reapply oil and polish with soft polish pad and rotex. The result is not glasslike obviously, but rather satin-like