You shouldn't have to bump all the levels up....I have not ever had to do that. Closest I get is with my turntable, it just has lower output to start with.
Your dac has sufficient output for the line inputs on the avr to get full volume, tho.
Can you take actual measurements of the spl (even with a phone app) at various master volume control settings?
Is this a new-to-you unit? Did you run the reset?