This may sound strange but maybe use the cap of a pen (long pointy part) to wiggle the trim down or out just enough to remove the back glass. Good luck Stem.

Try getting a putty knife or something else that is thin and rigid. Slip the knife between the trim and glass on the side that will lift. Gradually slide the knife toward the problem side while lifting the glass. This should guide the trim back into position and get it free. A second set of hands would probably help. I can send some pics of a bally backbox if you'd like. The top and bottom channels are individual pieces that are stapled to the body of the head. You could get a jimmy bar and pry one loose but your looking at repainting and repairing the damage.

If you have a set of these for setting the points on old engines/motorcycles I'll guaranty you can get a few blades in there. $4 at harbor freight or autozone. As far as removing the channel the easiest way is to score the top peice like in your first photo of the meteor and gently pry it out. It is stapled thru that piece, not the top of the head down. The bottom channel is groved to hold the base of the head and sides together with staples and wood glue. You would probably tear the whole thing apart trying to remove that end.

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Can you put up some pics of the outside surfaces of the back box. Top and both sides? Plus some pics from a little farther away to show perspective? I am assuming the Bally is like the Sterns but I don't know.

Here is a Stern back box I have been working on. I had to peel off the cheap pressed paper sides to restore with real wood. With the sides peeled away, I think it would be possible to slide the glass out sideways. These cheap pressed paper sides were stapled and glued on. One side peeled away very easy. The side had to be chiseled off.

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On the Stern, the two sides were not stapled or screwed to the top horizontal piece and it would have been possible for me to have just peel off the top by itself. I really cannot tell from your pics but it may be possible to pry off the top piece on your Bally. I'm thinking any damage would be minimal if you take precautions and since it is one top any visual impact would not be noticeable.

My suspicion is the top piece is two pieces glued together before being attached to the back box. So, if you have to destroy that top wood while prying it off, you should be able to salvage the "groove making" trim piece to a piece of replacement wood if needed.

And this: If you are not sure if the two sides are stapled, screwed, or nailed to the top piece, take a hack saw at the joining area and make a couple of cuts.

It is going to be a little work for you but in the end it is only wood.

I would go with the @cottonm4 approach. place a piece of 2x4 on the inside edge of the side trim piece and wack it with a dead-blow hammer. The trim piece for bally is better made than Stern, so it should come off intact. Once that's off, you can slide the glass out the side.
The trim piece is easily glued back; hold in place with a couple pipe clamps.

I recently bought a Seawitch with a plastic dart tip lodged into the top glass channel.

It was a bitch to get out.
Used a plastic pass card to push into the corner.

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interesting, none of my older bally's have a top trim and if I added one they won't fit.

I decided against gluing the replacement side strips I made on. I decided to use 5 flat head wood screws instead. The logic was that sometime in the future if one gets dinged up or damaged all it takes it to remove 5 screws and it can be removed and remade. The screws to do not look ugly and if you have the pin shoved into a line up you won't be seeing the screws anyway.

The next back box I am preparing to do will need that top piece replaced. I will screw it back on, as well. And now with this poster's issue, not gluing the top piece back on looks to be particularly advantageous.

My glass's wont fit with them on, couldn't even lock afterword's.
I've tried once and kinda ran into the same problem your having, a lot of
cursing and shaking to get it back out.

It looks like your side pieces may be stapled to the top. If so, this is where the hack saw comes in. Try to make a clean cut between the two pieces. Error on the side of top and try to save the sides. The top will be less visible of repair work. Make the cuts, pry the top off from the back side, left it up and remove the trim and back glass.

Don't glue it back. Just screw it back on.

I wouldn't try and remove the sides. The top has a tongue and groove that has been stapled and glued. If you remove the side you will most certainly break the joints and have to replace all 3 trim peices. This pic is from my fathom but I remember my lost world was built the same way.

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I did not say to pry off the top of the back box. What you pry off is the border piece that sits on top of the top of the back box. Sorry if I was not clear. But Thrillhouse shows that Bally used the tongue in groove method. That complicates things unless you would want to replace the top and both sides.

If you can pry off the top channel that would work I think.

Note to self: now that I see how Bally backglass frames are affixed to the backbox, I will never, ever, EVER pick up or carry a Bally backbox by its frame again.