Hmmm....my 59 truck has the windows in a frame. Why do you want to remove the frame? I would think a modern cut piece of glass with a bit more on it would fit your channels, if you had that felt trim in there. I wouldn't like the glass sliding up and down in the old steel channels. The problem is that the frame for the glass is what the regulator bolts on to to raise the window.

Unfortunately I am not familiar enough with modern doors/glass but would you drill holes or just make a bottom frame piece big enough to hold the bottom of the glass to lift and lower it?

If so, then you could probably just pull the frame off and be done with it but there would be some slop. You'd need to have the glass shop cut the piece the same size as your glass with the frame on it.