It's always tough coming up with alternatives to plastic. Modern merchandising and consumer expectations demand it. So sad!
When I was growing up, popsicles came in waxed paper, inside a waxed cardboard box. Yes, they got freezer burn if they were stored too long!
So I think the job for modern sustainable packaging users is consumer education. You need to manage their expectations, while telling them why they are such good people for using your sustainably-packaged product!
We managed to do a plastic-free farmers market operation, and we did a lot of value-added products, in addition to fresh farm goods. A "big think" for us was how to distribute dried goods (peppers, tomatoes, etc.) in sustainable packaging, in a way that was appealing to consumers.
The other vendors were all using ziplock bags for such things. Good! This is called "product differentiation!" We just had to explain "why."
First off, we made signs for our tent that touted our sustainable packaging. Then, we displayed our dried goods in large, four-litre glass jars, and sold them by weight, typically 40 grams. Your average consumer doesn't know anything about weight, so we chose that weight so we could easily compare it to something: "about the size of a lunch-box bag of potato chips," we'd tell them, and if they looked sympathetic, we'd snarkily add, "but without a piece of plastic going to the landfill."
Then, we weighed them out into brown paper bags, exhorting the consumer to take them home and put them in a glass jar with a rubber-sealed lid, as soon as they could, to preserve their crispiness and flavour.
I'm guessing that you have a "boutique" or "artisanal" product, as we did. Your customers are already paying extra for what they perceive as a premium product, so they are already receptive to messages like, "Best consumed in a week" or similar.
We also did fruit preserves, packed in reusable glass canning jars. They had less than a third of the sugar in commercial "jam," which meant they didn't last as long without going mouldy — sugar is a preservative! So we carefully mentioned that they should be consumed it "three weeks or so," because (minus snark, of course!) sugar was put into jam by evil industrialists so that it would last forever, so they could make more money, because sugar is cheaper than the extra blackberries they got from us!
If you have a receptive clientele, you'd be surprised at the minor inconveniences they'll endure to have what they perceive as a superior product. Yea, nothing works as well as plastic! Your job is to manage perceptions and expectations, so that your customers not only understand that, but see it as a benefit.