Bingo.Is it possible it's the room I'm recording in (it's very small), or is that not such an issue for close micing a cab?
Very big deal.
There's a bit of a delusion kicking round that being close to a source eliminates or reduces the room. Nonsense. You absolutely cannot escape the modal response of a room and the effect of near boundary reflections. They affect the sound at the speaker just as much as anywhere else in the room. The mic picks that up.
Move the cab around, see if you can get a more favourable interaction that way. There are lots of guides on speaker placement, as in monitors, and the physics is exactly the same for cab placement.
Also, given that your problem is currently with mids, 10cm thick of 60kg/m3 rockwool savages midrange and low midrange. It's near total absorption.