I was thinking of a mason jar using a foodsaver jar attachment. You can put the meat in there and pump out the air then freeze it, periodically pumping out more air as it freezes. In theory, the water in the meat should sublimate in the partial vacuum leaving you with freeze dried meat which should not require refrigeration. If you use an automobile hand vacuum pump which actually attaches just fine to the foodsaver jar attachment, you can draw much more of a vacuum then a foodsaver draws.

You could use parchment paper or Kraft paper i.e.: Butcher's paper.

To be honest, I don't mind using plastic bags. They are made from natural gas, but most natural gas are burned in flares because it's too expensive to put in the extra pipes, pumps and liquefaction plants needed to bring them to market and if they are not used for plastic, they are burned for energy. If you bury plastic in a landfill, you are sequestering the carbon within so with global warming concerns, sequestering carbon is good for the environment.

How about wax paper?

you could use a plastic container and reuse it again and again and again.......

Aluminum foil

I would use freezer paper, but it's lined with plastic so not any better. Is there any other option?

I've considered using reusable plastic or glass containers but it's impossible to find sizes to fit cuts of meat closely enough to avoid freezer burn.