Do you have, or know anyone close to you that might have, any camping/picnic stuff?? So cool boxes etc?
Is there a Scout Troop locally who might have a gas powered fridge or large cool boxes for camp that they aren't using at this time of year?
Is there any electrical shop locally that could supply one faster than insurance, and present insurance company with the invoice instead of letting them organise the replacement for you?
Is there a room in the house that you can turn off the heating to, keep it cold, and perhaps extra cool with bags of ice from supermarket? If you have regular large plastic tubs, with no holes in the bottom, they could work as emergency cooler boxes with ice packed in - wrap some blankets or spare towels around the outside as an additional insulation layer (in this case, keeping the cold IN the box). Or a plastic paddling pool or baby's bath or garden buckets (having been given a good wash out first)….all sorts of things can be pressed into use.
Would some neighbours have some space each in their fridges/freezers to take the most important elements for you - the smaller ones especially? (It might be a bit much to ask for a whole turkey space, but cream, cheese etc might be ok).
How cold is it outdoors? You could use the boot of the car, or the shed, even if the actual outdoors has too much local wildlife to be feasible. But if you have a garden box that hold cushions etc, you could put well sealed items in there safely.
Lots of "fridge" items can do fine outside the fridge, especially if only for a few days - cheese (especially hard and blue cheeses), butter, eggs, veggies.
Buy your milk daily for the moment, and buy ice while you are there too to keep the most vital things cold.
A thermos flask can work to keep cold things cold as well as hot things hot - might be an option for milk or other liquids for an extra day or so.
Sorry, that's a bit haphazard, just things I can think of hoping something might be useful.