I want to frame-challenge your assumption that aluminum is a poor choice due to difficulties in recycling. The linked question refers to "aluminum food packaging" such as soda cans, which is a composite of aluminum and epoxy. The epoxy is there to protect the aluminum from the food, and the food from the aluminum.
Aluminum foil is a different deal. And the frame-challenger there is to try to take a tour of your local {recycler | garbage stream} and ask to see their eddy current separator. You want to know if they have one.
Yo, magnets, oh!
So certainly the recycling stream, and maybe the waste stream, go through two interesting process.
First, they use magnets in the normal way you would expect, to yank out any ferrous metals - basically iron/steel. That's to keep them out of the next process.
Now, have you ever seen the inside of an AC induction motor? It has one moving part: a "squirrel cage" made entirely of aluminum. The fixed windings in the motor create a magnetic field that "spins" at 50/60 Hz. what can that do to aluminum? It can make electrons move in the aluminum, creating its own magnetic field which reacts against the first one. This works so well almost every AC powered motor is this.
Back to our eddy current separator, the garbage is dragged through a strong, spinning magnetic field. Non-ferrous metals "Jump!" ...while normal trash does not. At $3/pound for copper, this is worth doing just for the mineral value. Aluminum comes along as well, and now that they've separated it, it's no trouble to recycle it.
https://www.youtube.com/watch?v=K2KKmh-CYTg
You can freely dump aluminum into any waste stream where this is done.
Make it eddy-current friendly
The problem is a very thin sheet of aluminum foil may not have the density to pick up the magnetic field, especially if it's been mashed up in your waste stream and attached to other things.
So fold or crush it down into the densest, most compact form that you possibly can. Make it into an "aluminum nugget". Feel free to make a big aluminum ball out of multiple items, but past tennis ball sized, you surely have diminishing returns.
Metals recycle more efficiently than almost any other substance. They are, after all, atomic; literally atomic. Al is an element. The energy savings in reusing aluminum vs mining bauxite and smelting it is staggering.