I would love to leave them alone but I've got a cat.

I feel like the intuition is to get the container close.. Slowly... then snap it to the ground!

Don't do this. They're faster than you realise, and you risk crushing them, even when the gap to the floor is an inch.

Just go slow the whole way. They aren't going to know to scramble through a gap once it's smaller than their height.

How on earth are you catching them? I just use a broom and with a bit of encouragement, maybe a little glass of red, they climb on and I just drop them outside. Only spiders I knock off inside are white tips.

The bigger useful container you can find, the better, I've found. That way there's less chance of hurting them when covering them to take them outside.

I use a container with an opening big enough for maybe 3 huntsmen, I angle one side of it on the wall in front of the spider, then have a laminated a4 sheet that I rustle behind it to encourage it to run into the container. When it does I put the rest of the container against the wall and slide the a4 sheet in so I can move the container outside. Never hurt one doing this, but I've had lots of practice.