We ran into a similar problem, with the same scenario of selling our house to meet the requirement along with additional savings and a 401k. Then I found out from Medivisas and a few other people that the 401k is apparently too arbitrary to rely on, since "instantly available" can depend on whether someone opts to count the five hour time difference in operating hours as an obstacle. We also had a hiccup in that the family we were going to stay with till we found a place aren't geographically close to his job lead, and we got a great offer on our house much faster than we expected.
You can write an extended closing period into your contract; we had to just to have time to get all our stuff on a container ship. We worked out a deal with the buyers to rent the place back from them for 30 days and they were fabulous about working with us on that.
Medivisa suggested we go with our Plan B: I (US citizen) come over with my Better Half (UK citizen) as a visitor, get a place to satisfy accommodation requirements, he starts work and we can use the income option with the savings to back it up, I go back and bring the dogs and cats over, stay in the UK till the end of summer, and then go back to the US in the fall when the application rush hopefully goes down a bit and work while the application goes through. I'm renting a room in the US to store vending gear in from friends there as an address; I'll be staying with them when I'm not on the road between events.
That's worked well so far. I did get some extra questioning at EDI when I came back with the furballs, but I had my US vending contracts for this autumn and examples of the stuff I make to show them I'm legit, and they were happy enough with that. I also got a great lead on a festival to try vending at when I come back from one of the border officers whose wife is also crafty ;0)
Good luck!