Yes, sitting on the floor is GREAT. In fact, taking a nap in there is a wonderful idea (nothing less scary than a sleeping human).
Yawning, stretching - all good things. Especially if you're sideways to him and he can watch you.
Also, when you reach your hand toward him, hold your hand in a fist. It looks like a cat head, and is far less threatening to a cat than an open hand. You can also use baby food on a spoon - a hand with yummy treats in it is good too.

That said - we didn't try to force or rush the process, and we waited until they came to us. There's different thinking on this, and it's often hard to be patient and wait for them to come around. But a wand toy, at his age, is probably far more likely to entice him out from under the bed than a hand.
And yeah, removing the bed frame so there is no under the bed is a great idea. But we always let them have some hidey places - ESPECIALLY the crate you'll use to get him to and from the vet.

If the crate is his safe place, it works for all of you.

But if you're going to leave the bed there, I'd throw a box under it. And if there's a table in the room, maybe drape a cloth over it. And maybe put another box out with a flap down for him to have as a hidey place. The safer he feels, the quicker he won't need hidey places.
Another trick is leaving treats behind in the place you were sitting. It'll smell like you and be warm - and then he'll associate your smell with good stuff.

Also, get a t-shirt REALLY good and sweaty. Put it under his food dish.

You might want to get Feliway spray or the diffuser if you can afford it. This helps "de-stress" scared kitties.

Just don't plug it in near his boxes, or don't spray near the litter boxes.
I just remembered a new thing we did when introducing Chumley to our crew. He was separated entirely - we live in an RV and have no place to segregate a kitty, so we put him in a rented trailer. BUT apart from bringing blankets he'd been sleeping on over here, and blankets our kitties had been sleeping on over there (and letting everyone smell and investigate), we also brought over a poop and a pee occassionally and put them in the litter box! Might sound crazy - but we wanted them to get used to the scent of him being in their spots.
Now this I would not do that until you're sure he has no parasites (and honestly, I wouldn't bother paying for a fecal, I'd just have him treated with Revolution - it's a topical that treats for fleas, flea eggs, ticks, round worm and heart worm). But as poop and pee are both territorial markers, we figured getting over that scent hump would go a long way to smooth intros.