Thanks for the explanations!
My integrated amp (Rogers EHF 200 Mk 2) has 40 db of gain. The volume control is turned up much less with signal from the dac, than while using the phono preamp, which I presume means the dac has higher output; but (as I understand it) the gain from the phono preamp can be increased by switching the driver 12AU7 tubes for 12AX7's, if necessary. Which, maybe I should do anyway, as @Soix and @tomcarr imply.