Timothy, the solution MAY be less difficult than you thought: If you make a cage just big enough to fit the inside of the barrel, then make one a few inches smaller in diameter, They would sandwich the bag and might make it easier to pull out.
Ideally, the cage(s) should be smooth wall, to avoid catching on anything. For example, I have a big chunk of flexible, plastic like material sold to avoid scratching appliances, when moving them. It’s about thirty inches wide and about four feet long.
The larger cage would keep the bag contained and allow you to pull it out of the barrel. It may even provide enough spacing to allow air in to the barrel. Otherwise, you’d need a couple 3/8" hoses.
If the cage you have now is hanging because of horizontal connections of the wire, the solid might solve the problem. Ones I’ve seen sold to hold plastic bags open for filling with leaves make getting wet leaves out of things much easier.
If you try this route, you can check, for example, with moving companies and those who supply them, as well as garden and law care suppliers for the large plastic you can roll.