I guess the unhelpful answer, but maybe one to take heed of going forward, is that you spend more time on the overhead mic’s positioning to get a coherent, focused stereo picture into which the close mics can be placed that’s not going to subsequently give you issues.
I’m only listening on little dell desktop speakers here, but it sounds like the ghost note at 0:12 is coming from the right and the one in the next bar is coming from the left. That’s probably a phase issue - those ghost notes might have been hit on different parts of the snare, which has caused different patterns of cancellation to hit each mic and vastly change the resulting stereo image. And when the hi-hat opens, that washes across the stereo image too. The solution to that kind of lack of focus is to move the overheads - though I admit that Hi-Hats are very hard to properly pin down, and an easier solution is to take them away.
It’s definitely something that involves a bit of fishing around blind - you can get big changes with quite small movements - say, moving one side 5cm in one direction or another, or keeping the relative position of the 2 mics to each other but lowering their stands a little… but you’ll find a point when the kit seems to come into focus, and feel a bit more solid. As it stands, it feels like the overheads aren’t quite working together, like they’re presenting two different versions of the same drum kit.
Funnily enough, that can work well, if you really want to emphasise a wide and energetic, un-natural stereo spread. But you end up really needing to lean on the close mics to give the drums enough punch, with that method, and quite often there’ll be a room mic or two as well to help keep things focused.
I quite like the sound of the room in your recording, though! It’s got some life to it.
With this track, I’d probably start by narrowing the overheads. The narrower they are, the more cohesive that kit’s going to sound. I’d manually defeat the gate on the snare top on those snare ghost hits by automating it into bypass, and probably clip gain their volume up a little - not knowing the musical context the drum beat’s sitting in, ghost notes like that quite often need a little help getting through if there’s much going on in the arrangement. But that’s going to help centre them, because unless you’ve time-aligned the multitrack drums, that centre signal’s going to hit your ear before the wider wash of the less focused overheads, which’ll give you a perception of where the sound is located.
You could also look for some target frequencies in the overheads, a couple of notches to de-emphasise the snap of the snare wires, probably somewhere between 6-10k, but obviously if you do that you might lose life from the snare sound.
I guess my last idea would be, make sure you’re judging it in context. Does the ghost note drift problem matter much, once the rest of the arrangement’s in place?
I’ve had good fun with a “snick” mic before. You put it down under the hi-hat side of the kit, somewhere it can see the bottom of the snare and the beater head of the kick. You end up with an overall presentation of the drums that is quite papery and upper-middy with an emphasis on the transient snaps and quite a lot of hi-hat (to reduce hi-hat horror, I use an SM7b) then in the mix, you just slide up the fader until you hear it adding some top end excitement to the kit. Usually I found I needed to cut out some chesty resonances (all the horrible kick basketball bounce 500-800Hz, for example), but that it was a nice was of getting the impression of high end without having to pull it up in the overheads.