Depending on the dimension of the pack, this may work -

Go to a Wal-Mart, or any store with a Gardening Department, or look online for a "gardener's kneeling pad" - about $5, and they come in a variety of sizes.

Closed cell foam, so it does not absorb water, and quite stiff - enough so that it would provide a stiffener against the back of the pack that might give the pack enough "structure" to suit you.  I suppose you could attach some strings to the inside of the pack to tie the pad in place if needed, or even glue it in place?  but I'm thinking the pad alone would work.

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or this one, narrower but thicker -

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I have 3 different pads like this - one similar to each of the two I linked to, and another thick one that is wider.

I always bring one of these pads with me to use as a cushion to sit on around camp - a heck of a lot more comfortable than sitting on a log or rock without the pad.   I also use the pad in the tent, as an extension for my 3/4 length therma-rest pad - I put the gardening pad under my heels.  The smaller size weighs only 1.6 oz and the biggest size I have is 3.3 ounces, so you wouldn't be adding a lot of useless weight to your pack.  

I'd also think a nice thick pad against your back would be a lot more comfortable to carry than a garbage can.  But that's just me - maybe you'd like a garbage can poking you in the back ?  How should I know?

Anyway, it would be a cheap experiment, and you could always find some other use for the pad if it does not work out well for the knapsack.