I agree that bringing the treble side of the pickup up could improve the sound.
Yes, your pickups are already running in parallel. When the switch is in the middle position, it connects both of the end lugs to the center one, making a parallel connection. This is the usual setup.
I would think that yes, using a larger cap value (.1uf or so) would be better for the bass cut if you do that. Larger-value caps let more pass through. This is why the tone controls on bass guitars tend to use higher-value caps -- their frequency spectrum is lower, so you need to knock off more of the top end to be able to hear a difference. For the bass cut, since the high part is what we're keeping, the bigger-value caps would allow you to keep a little more of the original sound. I think this is a good idea in this case.
The whole bass-cut setup would hook to the middle lug on the 3-way switch on one end and the jack on the other, taking the place of your current master volume. How much this reduces your output (or what it actually sounds like) is anybody's guess; I've never actually seen it implemented. It was just an idea I had.
This is a separate idea from the treble bleed -- you're correct in wiring a .001uf cap between the first two lugs on the volume for that. If you want the effect for both pickups, you'll want to put a treble bleed on both volumes. Be aware, though, that if your volume has a treble bleed installed, you may not be able to get total silence. Even with the volume all the way down, a little bit of the signal will go through the cap.
Also, I notice nobody has addressed the idea that the extra bass sound could be a feature of the amp. What are you playing this thing through? Also, are you using heavy-gauge strings on the low end? If you think it's the hollowness of the body, you can also try stuffing it full of socks or something. Just don't put anything in there you can't get out, and don't jam stuff in next to the electronics.