Many thanks for the extremely helpful recommendations. I'm very interested in the Linksys LAPAC2600 too.
I keep finding out about more possible problems with the Ubiquiti kit, although I'm still very keen on it and the prices are great. One review I read stated that throughput per client was capped at 115 Mbps (presumably inbound) if the guest SSID feature was merely turned on, and this applied to non-guest clients too, assuming I read the thing correctly. I'm aware that this was a very early production unit and the issue may have been fixed, but this would be a show-stopper for me.
If the zero-handoff thing needs to be disabled for the devices to work properly with iOS then Ubiquiti is completely out. Because all my iPads and iPhones support 802.11r (and 802.11k plus 802.11v) according to Apple, then I would want to go for a WAP that has full support for all these three standards, so I'm adding 802.11r to the list, apart from the case of Ubiquiti if they have something that gives the same benefits reliably.
It looks like this is going to cost me an absolute fortune unless I sacrifice the high-end performance-related items on my wish-list. I'm not sure how many WAPs I need - certainly two, possibly four if I want to sort out outside coverage.