ah deepbreaths, poor you... sounds like you need a holiday but it'll probably be doubly stressfull being away !
When we go away I take all DS own bedclothes (so I know they've been washed without washing powder), we self cater so I can keep an eye on his food intake and we go when it's cool as historically as a baby, heat made his skin much worse.
What was your baby like in the recent heatwave ? Better, worse ? was his skin better after exposure to a bit of sun ? Maybe you could try putting a teaspoon of dead sea salts in his bath and seeing if it makes him more itchy, then you may know if he will be worse in the sea or better. It helps some eczema sufferers. What is he like with chlorine ? If you can answer all these questions maybe it will help you make a decision. How about just going for a week ? would that be a compromise ?
It sounds like you've been given rubbish allergy advice, although TBH I insisted on DS being allergy tested & was assured that the results are never accurate. He did however have a large amount of intolerances that I identified through doing an elimination diet. I did this under the guidance of a naturopath and a nutritional therapist myself, so if you were to go down that route you should get proper advice. Key foods for us have been dairy, goats milk, oranges, strawberries, potatoes and for a LONG time wheat, oats, tomatoes and corn.
He's 2.5 now and his skin is clear, but it's been a long hard slog so i totally sympathise with you.
I did introduce some Eskimo fish oil at 6 months and noticed a significant improvement but ultimately we have treated through diet and homeopathy. I've never used chemical creams so not familiar with any of the stuff you're using, but I can second the recommendation for Green People suncream, it's tolerated very well by DS and several other babies I know !
HTH and good luck with making your decision