During our weekending boating days going to get more ice was not an option. Every weekend was the equivelant to a RV boondocking weekend as far as utilities & services went.
The boat had 2 small fridges but we seldom used them. Could not see the point in putting cold food in a hot fridge which was off all week.
Food was put into the food cooler frozen, along with 2 or 3 1/2gal block ice. The food cooler stayed below deck. Drink coolers, 1 for the beer the other everything else, each had 3 1/2gal ice blocks. Drinking water went onboard in a frozen state. When possible the drink coolers were consolodated down to 1 cooler.
As suggested, a towel, prefferably wet, inside ontop of whatever, helps to preserve cold. Also, know what you want before opening the cooler. No shopping.