We're planning to sail away for the Caribbean next year. I'm aware of the cardboard/cockroach issue but haven't seen any specific reference to the carboard rolls that foil, saran, paper towels and toilet tissue are wrapped around. Do you advise eliminating these, and if so, how do you store those items?
I don't advise eliminating those cardboard cores - your life would be miserable and I'm not sure just how effective it would be. I think that the worst problem is with cockroaches laying their eggs in the cardboard shipping boxes, which are stored in dark warehouses. One thing to keep in mind is that in the tropics it's pretty difficult to keep your boat bug free (some of those cockroaches fly into your boat). So roach traps might be a good thing to keep around. But when you bring food back to the boat, lay it out in the cockpit in the direct sun for a while before storing it below.
More than cockroaches, watch out for weevils! They REALLY offend me.
Flour: squeeze the package. If puffs of flour escape, it's pretty likely that the flour has been invaded by weevils.
Pasta: Before buying, look at the pasta in the clear cellophane/plastic window in the box. If you see speckles (whiter than the pasta) on the pasta, it's most likely that it has weevils in it (those white specks are bore holes where the very tiny bugs bore into the food. You probably won't see the weevils until you bring the pasta home and pour it into boiling water, when the beasties die and float to the top. yeccch! When the food on the grocery shelf has weevils in it, the entire shelf is probably contaminated.
I remove all pasta from the box when I get it to the boat and put it in an airtight plastic container. Plastic bags aren't thick enough to keep weevils from boring into them. I do the same for rice, sugar, flour, crackers, etc. Less for the bugs to get into and feed upon.