You have some sympathy from me, OP: I have family in Australia and New Zealand who say 'Can I come and stay for a couple of days?' and then settle in with the intention of staying permanently. I've had to put them on buses and trains after a fortnight to get rid of them before I murder them. So I really do get it.
Given that they're total CFs from the sound of it, and this is the third time they've done something like this, I wouldn't be that bothered about the friendship. Also given the fact that they've wangled their way of out hosting you, I'd suggest they are really thick-skinned and quite difficult to insult. I mean, I wouldn't dream of asking to stay with someone if I'd refused to have them stay with me.
Do they only come to your area because you offer free board, lodging and taxis, OP, or are they in your area for a reason other than that?
I might consider contacting them and saying: 'Something's come up. I can accommodate you for three nights when you get back, but after that you're going to have to find an AirBnB.' Don't go into any details, just looked pained if they ask and say 'It's complicated...'
If they need to be in your area, I'd link to an AirBnB a mile or two away and say 'This looks nice.' If they don't have to be in your area then presumably, once they know they can't stay with you, they can go anywhere — a big city, a few days in Cornwall, whatever. So they'll be out of your hair.