Is this with no external preamp, jut the mic into the ZED?
You could try the line input which is also balanced TRS, but will take more level +34dbu.
If you plug the mic directly into a channel and depress the PFL button what sort of level reading do you see at the main LED meters while adjusting the trim or with the trim at zero? Also what is the mic you're using?
You should be able to set the input trim while watching the main LED meters to get the proper level. HPF should be on as well as the phantom power. Take EQ out to make sure you're not using a setting there. Fader should be at zero.
Just some ideas, hope that helps

Also LDC are extremely sensitive which is why you need to have them in a nice isolated space or booth with isolated stand suspension, not being touched or banged into, yelled or screamed into and of course a pop filter.

You mentioned "the trim knob is almost always close to 0", which is 14dB away from being set at minimum gain. Can you check what you get when the rotary gain control for that channel is all the way anti-clockwise (at the -14/6 dB label)? The Zed-R16 can handle -6dBu nominal signals (+14dBu full-scale) at the XLR inputs, so from what you report, your microphone is putting out somewhere around +11dBu peak, which I am having trouble believing.

What make and type is the microphone? What type of pad is it that you have tried between the mic and the XLR input? If you are supplying phantom power (48V) to your mic, you need the type of pad that will pass phantom power yet attenuate audio. Also, you can't use the line input (jack connector) to get an extra 20dB of attenuation if you want the mixer to supply phantom power.

Hey, thanks for the feedback and help everyone!

Boswell,

Sorry, I misspoke when I said "close to 0" before, even when I have the rotary all the way anti-clockwise I'm still finding that the lowest signal I can get coming through the mains when recording a guitar is +3db. I've tried a number of mics, obviously it's especially the case when I'm using LDCs like the Bluebird I have, or the AT4040. I haven't gotten or tried external pads to connect to the XLR, I was using the pad built-in on the AT4040s, which is -15db.

is your guitar amp really loud? are any of your auxes up?

I had read recently on GS (they who should not be named) a similar problem that the ZEDR16 preamp's were "too hot" on some mic sources and that one complaint about the ZED was that it had no mic input pad (like a switchable -20db).
Although nothing I know of ever came of that issue most people there thought there was something else going on beyond the ZED's preamp's themselves.

It would be interesting to find out if you were able to sort that out tcvermont and see if you can conclusively unravel that mystery.
If I had the proper tools available I would measure the actual direct output of the particular mics and then use a signal generator into the mic connector adjusting the generators output slowly upwards for different input levels and see if in fact certain source mics are too hot or sensitive for the ZED and in fact may need a pad under certain circumstances...
smoke