You have my heartfelt sympathy! I just took on a 5 rod allotment in much that condition and have a strimmer that gave up the ghost to boot.
I have had mine covered a while now and couldn’t find enough card and compost to cover so opted for mainly mypex as a stop gap to stop it getting even worse. I have planted potatoes through it and suffered quite a lot of slug damage and weeds finding their way through the holes. So far from ideal. Given the option I would definitely go for card and compost in preference and you can plant through that with less issues. However we work with what we have and so once my potatoes are out I will remove any remaining weeds, buy in as much compost as I can expect to shift and start doing it properly.
I think the key is to do what you can and break it down to bite size chunks. Enjoy!