Alternative is to go below 1g while inverted but this causes other problems like fuel feed.
Agree with you up to this point- any positive G should not result in fuel feed problems, and Airliners sre stressed to (IIRC) +2.2 -1 G with flaps up.
You can perform a constant positive G barrel roll from level flight, but it involes more than one G on the pitch up, less than 1 G (but more than Zero) over the top, and more than 1 G on the recovery.
And Bloggs- agree and disagree- started from nose high, an Aileron Roll is very simple (as in- apply Aileron!!). This is different from a slow roll.
What is different is that a in well flown barrel-roll the aircraft remains in balance, and so all stresses on it are on the nomal axis.
In either an Aileron or slow roll there will but tortional stresses that are unlikely to be accounted for in the design of the average people-mover.