Hi
Deluding here but can't help but feel a.little emotional reading your children ' s experiences. It brings back many of the emotions about being rejected by Cambridge a long time ago having being put in the winter pool by St John's but unfortunatly not being given an offer.
My rejection was a long time before the internet took off so wasn't able to find a community of Oxbridge applicants so find this thread in interesting.
With hindsight I wish I had reconsidered a reapplication after a year out. I felt that after rejection emotions can often run high and for me personally there was a desire to 'move on ' and I accepted an offer at a Midlands RG university.
Turns out I had not really processed the rejection and found some aspects of my university experience disappointing not least as the degree was not incredibly challenging (got a first) and due to clearing the course has to be suited to a wide range of ability in terms of a level tariff acceptance.
I would really consider a year out and re application seriously given the obvious talent of your children. I know this is not an easy option and very much dependent on individual experience but I think it easier to find closure on this journey if you have exhausted all possible avenues of entrance. There are a number of posts in various places about successful re applicants which are encouraging.
I am only posting this as I understand the sometimes strength of emotion about Oxbridge rejection but a cool look at things in a couple of weeks may allow some reappraisal.
If not reapplying I would have a considered thought about t he insurance offer and make sure it really is what is desired and the choice is worthy of your child's abilities.