I'm 02 and AED trained but you have to draw the line somewhere with what to take on an explore. I have one of the foil space blankets in the car but I've never felt need to take it into an explore - might be useful to have in some of the bigger kits.
On the Asprin / Ibuprofen question, I prefer Ibuprofen but some people go for paracetamol - some while back when I had a really nasty ear infection my doctor told me to take both and I said "What alternately ?" and he said "No, together". So having both can be useful
I'm a great beleiver in taking things with more than one use. Eye bandages were on one list - something in the eye means rinse with water, you can't do that with coke, so take water to drink. Saftey pins have loads of uses etc.
But I think you have to plan for categories of incident.
At one end you have the "Take tablet" / "stick something on it" and carry on type.
At the other you have the "Get professional help to the casualty" type - the person is not going to recover with your help alone, so your task is to keep them in the best state for the professionals - that means keeping airways clear, doing CPR, Stopping serious bleeding, watching for signs of shock. After that it is a question of watching and keeping the casualty comfortable.
In the middle "Need to sort that out when you get home", "Need to go to A & E" ... Some people seem to be trying to cover the whole of that segment...