Firstly, welcome to FlyerTalk supedaj!

You are somewhat limited with travel only during school holidays. Not just on peak Avios prices but availability generally.

You might want to think about split cabins - two in one cabin and two in another. Deciding who goes where is another matter - but it might open up more options for you. If you manage to snag two seats in First, then the other two can be guested into the lounge with you, so everyone benefits for the on-the-ground experience.

I'd also say take a look during the October and February half terms. Still relatively higher demand but it should be better in terms of availability for a week away than any of the main holidays.

Also, take a look at the Reward Flight Finder on ba.com - it might help. Unfortunately the Explorer Availability function is still not working (grr) otherwise that's a useful option.