How did you get from "starting in two weeks" to they need a couple of weeks to finish another job, so they'll start in April 2018"?
Over the time on my place I've tended to hire guys on price for the first job they did and assessed how they worked, then asked them to work on day rate if they're good. Yes, you could cynically say that on day rate they're going to take their time, versus price rate everything is a rush but I tended not to find that- people have a rate that they work at that suits their stamina, skill and speed of thinking, and it seems to become a habit. I haven't noticed my trades work at a significantly different rate based on how they get paid and day for the good guys seems to work out cheaper, because one thing all the price quotes include is a can-o-worms amount. My recent jobs have all been new builds, so very few cans of worms
Perhaps you can get these guys to do a smaller job first that is separate to the loft conversion, like a kitchen install. Either pay mode, doesn't matter, just to get an idea of accuracy of time estimate, pace and quality of work etc. It also gets them used to working with you, which will likely help things along for bigger jobs unless you're a complete pain in the arse to work with
in which case they can adjust their approach accordingly
ps; clients are generally a pain in the arse, and it can't be helped. They will always care a little too much about stuff that doesn't really matter, and I'm no exception - I asked the tiler to make sure he didn't lay any tiles with the same pattern (it was some pseudo marble thing but there was only about 16 different variations on the theme) within 3 tiles of each other, though if he was stuck he could rotate it so long as it was in a different row/column and he said no one has ever asked him that.. I had to ask him to pull a few off before he got the hang of it, but his grumbling at the start of the job had, come the end, turned into honest admission of what he thought were a couple of mistakes in placing identical tiles too close.
I left him to his own devices on randomising the next set of tiles he laid (some stupid hexagon shaped ones that are 8 hexagons stuck together in an H shape) and he's sorta got it but when I stand and look at it I say to the missus "see that one there with the white blotch in the corner- go 2 along and 1 up and it's there again. Now the one above it, go 2 along and one up and there's another repeat.. and so on most the way up the wall. Clearly they're in the boxes in a certain order, he's developed a method for making sure same ones aren't adjacent, but unwittingly he's put a pattern in."
If there are bits like this that you care about too much, get stuck in and do the prep, e.g. lay out and number the tiles, write instructions on the walls so your guys aren't going to have to chop and change