This is starting to look like the answer to preserving my embarrassingly large hoard of tobacco.You could also put the bags inside of a mylar bag and seal well.

40pc Mylar Bags for Food Storage With Oxygen Absorbers Label Resealable 1 Gallon | eBay
40pcs x 1 Gallon Mylar Bags (10” x 14”). Note: Oxygen absorbers will not extract all the air inside your mylar bag. 40pcs x 300cc Oxygen Absorbers. Two options for sealing the mylar bags: a reusable zipper seal and permanent heat seal.
www.ebay.com
They say you can use a hot iron to seal them, or an impulse sealer.