I've mounted all the way up to 56mm objectives on 20MOA bases over a Remington varmint barrel before with low rings (several times with 50mms as well). You can barely do it with a truck-axle aftermarket tube, but the factory ones will give you a bit more clearance. I'm currently running a Sightron SIII with 56mm objective on a 20MOA base with IOR low rings. I have about a short-and-curly hair's worth of clearance between the barrel and ojbective, not enough even to put on BC scope caps.
with a 44mm objective and low rings you should have about .200" clearance roughly. High rings will make it look pretty dumb IMO.
I like keeping it low as well. Here are a couple of pics to help you get an idea:
56mm objective in IOR low rings on a 20MOA base over a Remmy varmint barrel
50mm objective in IOR low rings on a 0MOA base over a Remmy varmint barrel