I don't have any answer to your Qs. just sympathy and my observations.
I have read your op and thread with a huge interest. I understand London, London jobs, Londoners and have come across pp not dissimilar to you and your situation.
You are getting a lot of diverse opinions, advice and help; which is all what any Londoner would need. so well done for starting this thread. so this diversity is what you need to open your mind to all possibilities.
I agree with those who say, once the next year funds for private edu are gone, then you will become desperate, and then maybe it will be at that stage that you will think to implement some of this advice and/or really change your situation.
at the moment, you seem fixated in what you and dh are doing and wanting to give it another year to fail (or maybe to get the break that you need.)
one thing though, this thread is a reminder to those with school kids for one parent to remain in a permanent position and not have them both as contractors/freelancers. yes, money if great when contracting, but many many sectors do go through periods (even 10 years) where contractors aren't required.
I said I had no answers: Oh, I do know that a lot of permanent jobs go to contractors who have been contracting for the company or even in same role. This has to do with a fit/ and employers not wanting to take a huge risk on someone unknown with a history of contracting.
Yes, a lot of pp (not all) are contractors because they are terrible as employees and usually only look for permanent jobs when they cannot find contracting jobs. As you in your case, you are only applying for permanent jobs because you cannot find contracting jobs. As pp said, employers would Q your commitment.
Another observation is that: I know you are building the product together, but you seem to align yourself too much with DH and his experiences? Sorry if I got it wrong, but you seem to lack your own true identity.
Lastly, I am shocked you guys are getting £1500 p/m for a day's job but yet, your title says "No job for 12 months in London'. Combined with kids still in private school (I wasn't concerned with this that much, but combined with first sentence) I think you have unrealistic expectation about life and you are holding on to a lifestyle you simply cannot afford, to keep up with Joneses. Yes, I once earned £1mil from work, but even I wouldn't call getting £1,500 pm as nothing. I even subtracted tax from it, to be more generous with your approach, but still a couple of hundreds a month are not nothing.
Going back to opening your mind, I think I meant broadening your mind, see the world differently, and I am sure something will turn up. Good luck, but sorry to say it is your mindset which is holding you back. I have also admired that you seem able to identify issues, tackle them and keep up the resilience, but I think that is also driving you into sticking to just wanting one outcome.
Even this VC funding may just end up with a false hope unless someone is willing to pay you millions to buy your product, which seems to be your end goal?
I would separate your and your DH approach to this (as it is clearly not working although I see the temptation to think 'we are nearly there') and maybe one of you will get lucky.
Sorry to ramble, but I was hoping one point from this long post, might stand out and help you, as I have met pp like you irl in London and it takes a lot for them to change anything.