The only dying I've done was mostly after I turned the piece. I used a q-tip to paint the blank. The dyes I used came from Lee Valley and were mixed with water. You can probably mix them with alcohol for faster drying.
I also tried soaking a whole bunch of plain tongue depressors (Large Popsicle sticks) in the dye. They somewhat soaked right thru since they are quite thin. I let them dry for a day or two in a warm area before layering and gluing them together. The results was a cheap replica version of dymondwood. I could have also used the dye in a solution of Minwax wood harder, but I didn't have it available at the time.
As for the H.F. pressure/vacuum pot, there's an article somewhere in this site about stabilizing wood. It's the same concept. I just got mine set up so I haven't tried it yet. My first attempt will be to dye and harden corn cobs, once I can get my hands on some. I would say mix your dye and put the wood in, then pull a vacuum before releasing it. Depending on the wood, you may have to do several cycles. I would suggest mixing the dye with alcohol, acetone or wood hardener (if wood is soft). They tend to dry quicker than if mixed with water.