Just picked up on this item, but what a truly brilliant article, people moan on here sometimes about who said what to who but this shows the depth of experience there is out there to anyone who gets into a mess doing what we do.
Luckily over the years I've been doing this, all the shrinkers were down to flooded carpets and not me.
But what we did in a situation like this was to make sure the carpet was dry, double gripper the room, (you get more surface grip)and then fit the doorway first with a wide bar if it needs it, and latex the back of the carpet and the gripper/bar in the doorway, let it go off, so it is dry and fit it then, nothing will move 2 dry latexed surfaces and then fit the rest of the room, with a power stretcher if you can,not a knee kicker.
This was shown to me by an old experienced fitter and it allways worked, the reason to do the door first is because 'she' will allways see that area when they walk through and not the rest of the room with the furniture in.
Why a power stretcher? They stretch all the carpet along the lenghth , but a knee kicker only stretches the 2 or 3 feet behind it. Its a 2 man job you will probably only find 1 from a commercial type fitter as they use them in pubs, hotels etc etc.
Good luck with it and again what a brilliant item.
Murky