In the UK PEL offer archive quality boxes for tape reel. But as you suggest, they ain't cheap...From a conservation point of view I wouldn't be using plastics - particularly soft plastics. Having lived in the US I know how very easy it is to get this kind of product there - Conservation Resources Audio Tape Boxes – #551MC- 771MC-1111MC - are inexpensive and good quality. You might try archival material suppliers in the UK but expect much higher prices. DGP
Only if the paper was gas tight - which I suspect it is not. The plastic in ziploc bags can/does do dreadful things to photographic materials. Cutting a large piece of archival card into a cruciform shape and scoring/folding it to enclose the tape reels might be a solution but the corners could let in dust.Perhaps wrap them in museum grade paper and then put them in ziploc bags while you find a better solution.