I'm in the same situation (family of 4), and some thoughts I have come to have on the topic are to strongly consider not being locked into school holidays -- how big of a loss is it if my kids happen to miss a few days of school (especially that they are in elementary or middle school now). They may get more long term benefit of a new cultural experience than they would have sitting in class (I'll admit that I had near perfect attendance going through school -- I don't think I would have been too much worse off missing a bit more if it was to travel).

Secondly, I've started to weigh the cost/benefit of either booking some tickets at the higher level as has been suggested or even deciding to pay for a one of the tickets if needed. My strategy would be to have the paid ticket be for my spouse or me so the miles earned would be useful for future trips. While I value a free vacation as much as the next person, I've come to think its a matter of trade-offs -- do I want to wait and keep digging for the absolutely free flights for 4 or get 4 for the price of 1 and actually have a vacation planned.

Just my .02 on the topic...