[Raak] I did receive it - the darn webmail form constantly auto-refills the zenxxxxx address every time I tweak the email (such as by adding an attachment), and it's easy to fail to catch it. My short answer to the jelly question is that I don't think it matters because even when the numbers rise, their 'rail number' still ticks down inexorably. Showing that numbers can rise as high as they like and yet it still doesn't help them escape is a key thing I'm trying to make clear. But you exposed an area where I'm not saying what I really wanted to - so I'll be fixing that and sending you a reply, probably at the weekend. I was also sidetracked into wondering whether numbers in the sequence have a provable 'high water mark'. If you could show that no number n can ever rise above, say, 2^n, that could be another clincher. 2^n ought to give sufficient headroom, right?
[nominative etymology] There's a place called Kenovay on the island of Tiree, which looks like a phonetic rendering of its Gaelic name Ceann a’ Bhàigh, which means "head of the bay", or Bayhead ("the parst of a bay most distant from the larger body of water with which it is confluent"). There are a couple more Ceann a’ Bhàighs and Bayheads in the Hebrides. So that could be the origin of the name.