HighestOlive: I'll give you my take for what it's worth. Personally, it sounds like a good drum kit to me. I can sit here and tell you 100 things to do differently but that would make the kit materialize into something *I* would like.
What you have here in my opinion, is a good classic rock drum sound circa 60's and 70's. A sort of Ringo from The Beatles sounding kit to where whoever was playing them, didn't really hit them with any conviction. This means this particular kit wouldn't be too great for anything hard rock. LOL! But for light rock, country etc, I see no blatant errors in this sound other than I would like to hear a little more tom panning and a little less cymbal separation. Meaning, your toms don't seem to pan much (or at all) and your cymbals are everywhere due to your room mics or over-heads.
Now the other thing I'd like to address. It is near impossible to tell you "you need to do this that this this and that" with a naked drum kit. It is best to always listen to it while being mixed in with a song. We can come up with the greatest sounding instruments known to man by themselves....that doesn't mean they will work in a mix of other instruments.
In closing, I would say that you have the makings of a good sounding drum kit here. I wouldn't change a thing other than working on the panning and then see how it sounds on a song with a little compression and processing etc. Nicely done....good luck to you.
-Danny