Baling Aluminum Cans

I am looking for a way to bale aluminum cans in a vertical can crush baler without using cardboard to hold the bale together on the top and bottom. I am currently cutting the cardboard out after the bale is removed from the machine and everything is holding together once shrink wrapped. I guess my main problem is getting the wire through the grates. The cans are sinking into the grates and I am having a hard time getting the wires completely through to finish tying the bale off.

The bales are being sent to a scrap metal company for reprocessing. If I can get the cardboard completely out of the bales on site, I can send the bales straight to a smelter and increase profit.

Any suggestions are greatly appreciated!

I am not 100 percent sure what you mean by a vertical can crush baler, but i assume it is similar to the balers I have that are vertical, ive never baled cans but I'm wondering if you could put a piece of 1x1 steel tube in the 6 bale strap slots and leave them in while you bale and remove them when he bale is full.. in theory that will leave a void in the bottom large enough for you to get your bale strap through. Then remove the bale and shrink wrap... what do you think, decent idea?

We have not had good luck with doing this.
My buyer doesn't have a problem with cardboard on the top and bottom as long as I get a tare on the cardboard(We use cut up gaylords)
We also don't use wire, I prefer using banding.