"There is nowhere near the swarm that is strong enough to hold a ladder...and I can't afford a fine for cutting the tree! I should also point out that my apiary is directly underneath the swarm - so can't drop the swarm onto them..."
I've had the same problem as you for the last 3 days, except that my trees are willow (no TPO though) and the swarm decided to settle over the chicken run, on a branch which is too flexible to put a ladder against, and too high to use my usual windsurfing-mast-with-nuc-attached:
I ended up using a small crossbow to fire some fishing line over a branch, then tied it to a rope as suggested above, then I raised an open poly nuc (ie no lid) underneath (picture below shows me lowering nuc after having left it in front of nuc for a day with old comb in with no success, but you get the idea):
I raised the open nuc right under the swarm (eventually!), then used lengths of 2x1 screwed together to hit the branch from below. I found you have to do this *hard* so you get clumps of bees falling into the box, and at some point (hopefully) the queen.
I found the best thing to do was to wait for them to regroup on their branch for a few minutes, then hit it again from below, so that further clusters fall into the box - if you don't wait, and you hit the branch again too soon, they just fly off.
I then lowered the box, found the queen, put her in a queen clip, put her in the nuc, and left the open nuc under the branch, but on the ground, so that hopefully the smell would waft up.
15 minutes later, the branch was bare - you could actually see it thin out as the bees flew down. You could hear the bees fanning quite hard.
Yeah baby, show us yer Nasonov!
You have to do all this quickly, and yes it was a total PITA. It was also counter-intuitive, as putting an open box under the bees is the opposite to what we usually do.
