I did try the ground lift.
I realize that I said I’m not a DI box connoisseur, but I do understand what a ground lift is, I understand the difference between balanced and unbalanced signals, and I get the high to low impedance thing.
My real question was whether a decent (Radial) DI box could produce a significantly better result than a cheap (Hosa, Behringer) one. My answer, based on my experience so far, is yes.
It will, especially in edge cases. Most of the time cheap DI boxes will be perfectly adequate and you won't notice any difference.
But using longer cables or having some specific environmental sources of EM interference — you're moving into edge case territory and it's no longer clear-cut. Cheaper boxes will have audible high frequency roll-off and/or won't reject some sources of EM interference.
In my church, there are two locations where I typically attach the mixer. Two XLR sockets equipped with a variable preamp in each location.
One location has a noisy ground loop even with some class II devices, while other class II devices are completely clean.
The other location has a less noisy ground loop.
Both locations provide phantom power that cannot be turned off (this is important).
In the former, I use a Behringer HD400 (1:1 transformer) and a Behringer DI-20 (active DI box) to get rid of the noise. Alternatively, I can use a Triton Audio Phantom Blocker in place of the DI box, and it works, too.
In the latter, I only use the active DI box, and all noise is gone.
Neither location actually needs ground lift (the former already breaks the loop thanks to the transformer, the latter doesn't need it).
I could get a passive DI box that would do both (particularly since it doesn't provide a signal into a long cable run as there's a preamp available), but a good two-channel passive DI box is expensive, and some the cheap ones apparently have a problem with phantom power. Maybe they eventually saturate because hum gets progressively worse the longer they're connected.