The key thing is to buy things that haven't been chilled or washed. Such produce is freely available in the Canaries as long as you stay away from supermarkets and go to the central fresh market. Order everything from one stall (check them out first), they usually take orders and deliver to the boat.
Also some things keep well, others don't whatever you do.
e.g. apples, oranges, potatoes, white cabbage keep well.
Leeks and green peppers don't.
Store everything in plastic baskets that allow air to circulate. Check every few days for anything going off and eat it or chuck it.
Buy a mix of ripe and (mainly) unripe fruit. Keep citrus fruits separate from everything. Also keep bananas separate. They both affect other things ripening.
Everybody says turn the eggs over occasionally but there's no need, the boat's motion shakes them up nicely. The other old wives tale is to wash everything before storing - DON'T. If the potatoes have mud on them leave it but make sure everything is dry.
If you are in Las Palmas one other good thing is that El Corte Ingles sells frozen vacuum packed meat, it lasts for weeks in the fridge so it's worth stopping even if you're leaving from the Cape Verdes.
Our experience from two Atlantic crossings was that squashes and potatoes kept well in a plastic crate on deck, despite regular dunkings in seawater, if protected from direct sunlight with a bit of cloth. It also gets round the problem of rotting potatoes in some hidden corner of a locker, discovered weeks later!
Apart from that, lots of temporary hammock netting strung across the saloon allows fruit and veg plenty of fresh air, makes inspection easy, and prevents bruising from the constant rolling.
You can also buy fresh herbs and plants like lettuce from one of the market gardens in the Canaries for next to nothing - we repotted these and managed to have fresh greenery all the way across.
We have, so far, always washed all the fruit and veg (including potatoes) in a dilute chlorine solution - with careful individual drying and airing, we haven't had problems with things going off too quickly.
Fully agree with the idea of vacuum packing meat. Cheese can be vacuum packed very successfully too - helps with keeping it fresh.
We found that hard veg (potatoes, carrots, etc) lasted really well if wrapped individually in newspaper. Also had success with keeping cheese in olive oil when not using fridge. Our cheddar lasted for weeks but did taste a little strong by the end. You can buy tinned cheese in the Caribbean...it keeps wonderfully but tastes a bit strange and won't melt...I think it may be more plastic than dairy. A great hint we were given was to brush loaves of bread in vinegar and then wrap in cling film. We were sceptical but it really worked and the bread didn't taste odd.