We can't see how the Door glass to metal channel rubber seal will fit in the channel with the glass.
The piece of wood in the channel is about 3/16 and the glass is just shy of 1/4 inch.
I cut the lip off a small piece to see if it would work any better.
Also where would you apply the weatherstrip adhesive, in the track, between the rubber & glass or both?
I use Locktite PL-S30 Flashing sealant in the tube. It cures to a soft rubber and fills in the channel completely. The reason is if you get water in the channel it has no where to go and will rust it out quite quickly. The part you cut off is for a weather seal when the window is closed to help keep the rain out of the door. I found the whole thing inadequate and made a seal out of flat rubber. Nobody notices the difference and it actually serves it purpose.
That channel doesn't look like it's shaped correctly, I assume it's repro (no former rust signs on it). The original way most glass was installed in channels was with setting rubber, which was oiled, placed around the glass, then the channel pressed on. The oil swells the setting rubber, and keeps it in place. the repro lipped rubber may or may not be made correctly to do that!
All the original channels I've seen fit better to the glass and have a more "squared off" bottom.