Flipping the door is no help as the screws are screwed in through the felt runner from the top.

I got some contractors shims and lightly hammered them at the space between the glass and top door lip to no avail even with using WD-40. I may need to take the door off and flip it upside down and start taking the little screws out. I am afraid since they are external hinges (it's a UK '68 Mark II) I may screw them up so I left it alone for now.

If you can locate the screws they are usually rusted solid so it is best to drill them out. If you have trouble finding them and they are long enough they may be sticking through the frame slightly underneath.
As the windows are stuck open maybe try using a hammer with a wood block (gently) to soften the blow to jar them loose, it sounds brutal but if you can get them to move slightly they may loosen up.

The rubber / felt window channel and the chrome trim strip under it are held in with some tiny self tappers into the door. Sometimes people use pop rivets.

Usually 2 at the front and 2 near the back.  Again, usually in the channel in the felt that the glass doesn't slide in - so that the inside channel at the front, and the outside channel at the back.

Do the chrome trims under the windows have lots of holes or just two  ? (early cars had lots so that window could be locked in many positions)  Perhaps the window catches have broken- the post 1964 black & white plastic ones have a bad reputation fro seizing / breaking.  The earlier chromed metal ones are much more reliable.

BTW have you got a Haynes manual ? 

There are some screws that hold the bottom trim piece in. They are in the felt. Maybe they’re not for the trim piece but rather for the felt

Try removing the latches, and see if they will slide.

Both of my '68 Austin Mini's passenger side sliding windows are stuck open. The car came over from the UK with all it's papers 11 years ago and I noticed that door (left side as it is right-hand drive) was replaced in 2005. So it could be anything related to that, but no WD-40 or anything else will free them. I do not notice anything visibly wrong with the door except a slight gap on the underside between the bottom edge and the rocker panel. There are no comments about this in my manuals. Is there a way anyone else has had this problem and will I need to take the door and window frame apart to see what's up with this? Are there any adjustment screws?