The way recycling of bottles happens in Norway is actually quite interesting and would be very easily adjustable. Basically there's a tax on all drinks containers, but you can "buy yourself free" from the tax by demonstrating collection rates, and the tax is higher than the cost of recovering bottles for recycling so in practice most distributors and retailers are part of a collective recycling scheme that requires all of them to accept bottles for recycling. It stands out to me as a great model for relatively non-invasive government regulation, in that it's setting a cost to account for an externality, provides a relatively cheap option to mitigate it, but if another option works better for you, you can choose it. If you don't want to participate, you pay and other people get the tax deduction when people return your bottles elsewhere anyway.

All that'd really be needed would be to adjust the initial tax rate to properly depend on the relative environmental cost of failing to collect different types of products.