Would trying a more minimalist miking technique be something you could experiment with. I've had great results with the Glyn Johns 4 mic (and 5 mic) method. Another thing that others have stated BLEED ISN'T ALL BAD!
Basically you have two mics as overheads. You position one over your rack tom(s) pointing at your snare. This mic is usually about 2-3 stick lengths above the snare. The other mic is 2-3 stick lengths away from the snare drum only this one is about 4-6" above the floor tom pointing toward the snare and hi hat. (if you do a google search you can find some images of this to figure out what it should look like)
Next you mic up the snare and kick drum. Your Beta 52 and SM57 would be adeqaute in getting the job done. Not my favorite choices but hey you have what you have and I'm sure a Beyer M201 for the snare and a Heil
PR-40 on the kick are probably out of the question.
Now if you still want some more ambience take one of your room mics and place it in front of the kit (FOK style).
Try to get the best sounds possible with as little as possible. This technique hardly takes long to setup and the results are oftentimes better than miking up every last stinking drum. Although I'm probably partial to the method because most of my favorite drummers growing up were recorded by Glyn Johns.
Learning to properly place mics is one step.
Next you need to focus on the actual performance and source. I know it sounds simple but how does the actual kit sound on it's own unmiked just in the room. Perhaps you need to move the kit to the center of the room. Perhaps the drums need new heads or to be fine tuned. So many variables here. Or better yet, maybe the drums aren't in tune to the song(s) you are recording. Also you can't blame mics and gear for a bad take or a bad drummer. If the sound in the room isn't happening (meaning mistakes, improper balance let's say all you hear in the room is the snare or a certain cymbal, whatever it WILL NOT sound good on tape). Sometimes the quality of drums and cymbals use can also influence the final sound. Don't expect a $200 sound percussion kit with an $80 cymbal set to sound like a well tuned custom north american maple shell kit with a set of $4000 custom cast cymbals.
Now I've brought up the room a little bit. Drums are very tricky to record (possibly) one of the hardest sources. But it can be done easily.
You will need acoustic treatment to optimize your drum recordings and make it as easy as possible. Drums need the following treatment BASS TRAPS (easy to make your own search the thread or google to find out how to DIY). They need broadband absorption / gobos (also easy to make yourself simply search). Last you may need some diffusion treatment to help with cleaning up the high frequencies. Acoustic treatment doesn't have to be expensive and don't be fooled into spending hundreds on a silly foam kit at your local guitar center. Building your own will be cheaper and work MUCH better. Plus your own building can customize to your own needs and work best for your room.
Broadband absorption can be as simple as hanging packing blankets on the walls to cut down on reflections.
The room has to sound good for your kit. Now you don't want to get the idea that you are killing all tone in your room or making it sound dead. Because you don't want a dead room to record in. You simply want to cut back some of the reflections and clean up the sound. You need some life for your drums to breathe in.
Best of luck. Any pics of the room with your setup or soundclips would really help out here.
I think the real issues you are having aren't bleed but rather phase issues and comb filtering. You probably have too many mics up on that kit and they aren't positioned well in respect to the other mics and in relation to the room.