Personally I would say that 240,000 Avios plus GBP 2K in taxes (so roughly 500 per person) is a pretty good deal for a LH round trip to the US in Club.

At the end of the day it's a subjective decision for the OP whether they feel it's a worthy use of Avios. Yes, there are some downsides in terms of having to start in the UK and APD etc. However, to be able to take the family to the US in J for a relatively small cash outlay is extremely generous!

OP, ultimately it's your call but if it was me, I'd be doing it. Easy come, easy go on the Avios.