I have done this before on many different types of air bubbles and I have also had success with this on a mylar bubble on a insert.
This is not for the faint of heart, I am a professional Automotive painter for over 30 years so I have many experiences at this and many other kinds of paint restorations that would require repair and not a refinish.
You will need a syringe and your wife's / girlfriend's clear fingernail polish, paper towels, clear scotch tape, and patience and a period of time. Catalyzed automotive clear coat works the best but is not the most user friendly or cost effective. Leaving your playfield in the machine (gives the angle for the air to escape) You will need to make a pin prick at the top most point of the air pocket. Then you will take the syringe (smallest one you can come up with) and get some of the fingernail polish in it just like a doctor would from a bottle of antibiotics. Next you will "inject" this into the air pocket making the insertion at the lowest point, opposite of the air escape hole you made previously. This will fill up the pocket and air will escape out the top hole. Stop just when the liquid starts to leak out of the top hole. Have your scotch tape ready to cover both holes, while leaving the needle inserted cover the top hole first, do not apply any more pressure than needed to seal the tape around the hole. Then with your tape ready remove the needle and apply tape.
Now you play the waiting game. Fingernail polish is a air dry type of coating and will take a while to "harden" as it is semi sealed under the mylar. I say semi sealed because almost all surfaces are porous to some degree or another, it will take some time for it to harden by way of evaporation of solvents. How long depends on the Temperature, humidity, thickness of the application, and in this case how porous our mylar is based on its overall condition. Any liquid that leaks out will need to be smoothed lightly with 1000 to 1500 grit sandpaper after it has cured or dried. This could take a few days so be patient, and after it is smoothed you will use the Novus 1, 2, and 3 to shine it up and get out the small scratches from the sandpaper.
So as I said this is not for the faint of heart, it takes some skill and practice. Do one at a time and start with the smallest out-of-the-way one and see how you like the results.
I also want to note here not all fingernail polish is the same .... if you need to go buy some do not get the .99 cent bottle, pay more like $8 for the good stuff. It will have less solvents and more solid product to its composition. This will be easier to use and will not leak out so bad and also dry quicker. Also with less solvent in the product you will have slim to no chance to melt a insert or make the silk screening move under the mylar.
PLEASE ... Please do this at your own risk and responsibility and if you think you are not capable to do something like this then DO NOT attempt. Call the cousin that paints cars for a living and show him what you need done, buy him a 12 pack and cook him a burger and let the professional handle it.