I love the supermarket cardboard box idea and wait to hear how it goes. I think I would use two per plant, given the root spread of the plants themselves.
I am impressed with the area you intend to convert. We have slowly been contracting the area of our garden and have suddenly decided to make some raised beds
Past posts on here will show my former views on raised beds as being unnecessary to the growing of vegetables - on most soils and for most people flat row crops are far more efficient. However, age insists we give it a try, so we are currently building 5 beds in our polytunnel. Each is 1m x 2m, and made of scaffold boards standing on the old growing surface, which at least doubles the depth for roots to run.
The relevance to what you are doing is that in order to fill these beds we needed quite a lot of compost - nothing like you will need, maybe about a tenth?, but it seems a lot. Anyway, Charles Dowding keeps mentioning mushroom compost as being good both for beds and as a mulch, but I have never found any available locally until now. The recommendation is to buy a 10 ton lorry load, but our access for lorries is limited, so we went for 1 tonne dumpy bags (1 cubic metre) of mushroom compost, two of them, collected in our sheep trailer. We can get the trailer to fairly near the polytunnel, but it has to be barrowed the rest of the way. The dumpy bags cost £75 each, but a lorry load would have been very much cheaper proportionally, had we had the access. We have used about 4" of this compost per bed, with about 2-4" of finely rotavated well rotted sheep manure from their field shelters, plus some molehill soil, spend multipurpose compost, seaweed meal and wood ash, and for the beds intended to grow beans and leeks this year, some partially rotted poultry manure as the very first layer. This is filling the beds wonderfully, but we have yet to see the results once the crops are growing. I think only one of the dumpy bags will be used for the beds, the rest will go for the row crops of tomatoes, climbing beans, squashes, cucumbers and brassicas. We use the poultry manure outside for potatoes and broad beans, and the sheep manure where we need well rotted manure.
I know the mushroom compost sounds expensive by the dumpy bag, but if you could get a trailer load delivered and keep it protected from the weather I think it might help with the bulk compost you need. It's great stuff, still with most of the nutrition in it, although it has of course grown a mushroom crop.
I have also found a biodegradable fabric which looks like black plastic but which turns into Co2 and water after a few months of use and I shall grow my bed crops through this. It's sold by LBS at £475 per kilometre, but I bought 20m for £25 from Garden Naturally
. Again, I don't know if it will work well, but I'm happy to invest that much to give it a trial. Meanwhile we are using the huge pile of cardboard left over after we had a new kitchen fitted - huge pieces which cover the beds with one piece (bit of an expensive way to acquire it of course - never again
)
I've been trying to go no dig for a few years now, but my less decrepit husband, Mr F, has always insisted on digging. He is quite excited about the beds trial though. One of the best bits about growing your own food for me is the experimenting you can do, trying something new each year and evaluating the results.