So, was really excited to approach this one, as I love the whole NY mixtape scene and early 2000s era.
So first thing I needed to address was those DRUMS - like you requested, and as I'd expect.
So they were really lacking some weight and punch and as you know, we really want that kick punching and that snare cracking, want them drums jumping out the mix.
SO, first, I approached this with some dynamic EQ to poke the kick thump and snare crack(and punch) when they hit. I used dynamic EQ and transient shaping to achieve this. This helped a lot. important: drums were mostly provided as a drum stem file ... kick snare etc as one file, so no individual control.
Later on in the mix, I decided it wasn't enough, and I also reflected on a different method I may have liked to try - originally thought of mixing from the start, but decided to just try add it where im at...
So DRUMS pt. ii. I then created a duplicate of the drum track at least twice ... first dupe I hi cut all the way down to just the kick thump, maybe massaged it a little, then raised it up until that kick weight became present... I then did the same with the snare. I basically re-mixed the drums from the drum stem that was provided.
Interesting to note... I had a transient shaper on the drum buss to add the transient punch in... reducing the sustain helped, HOWEVER... boosting the sustain did not take away from the punch, but brought the drums to life a bit like you would hear in a Just Blaze track, brought the details out. So I kept it.
Crashes
So, for me this is somewhat second nature to mix, as I use them a lot, and in this style. Basically, I find where I want them to sit from L-R... usually I pan; panning makes them very audible, quite an aggressive sound, so i was able to turn them down a bit as the width keeps em loud and big, I also wanted to keep them bright enough to not sound like smushy nonsense.
So... my approach, I find the listening/playback that will highlight the most harshness... I then boost their high/air frequencies until it sounds broken or painful, I then back it off until it sounds fine. --- I then find that, with the panning etc, they usually just sit right. they usually have a few db range to play with at this point to either have them slightly louder or quieter to taste without losing their impact. Maybe adjust to meet the tone of the record. Could even very very high cut just to round it off if you've got enough brightness but want a bit of darker quality.