The aluminum foil won't be heat resistant enough. Sheet metal is what you need.  I think, if you have not used a wood stove, you may not understand how EXTREMELY hot they can get very quickly with an uncontrolled air draw.  

It's dangerous. You MUST be able to shut them down completely to slow down that fire.  

I understand wanting to use it with the doors open, but that's while it's getting going--or once you get the fire where you want it and get the draw going properly.

Also, have you cleaned your chimney, and have you cleaned out the stove pipe to make sure there are no bird nest, rat nests, animals living in there, etc?  That's a chimney fire waiting to happen.

This sounds like you just want to use what's there and not spend a bunch of money, and I get that.  But burning your house down is behind door number 3.  Don't choose that door.

Maybe you could get a whole replacement door from Franklin.  I have a hard time believing there is no "replacement" solution as many stoves as they make and as long as they've been around.

Wood stoves are wonderful.  I grew up with one in the basement like you have (though not as nice as a Franklin. This was just an old tin stove).  And it's very relaxing, doing exactly what you said.

Hope you can find the manual and get your door fixed so you can enjoy it safely.