I recently created my second vessel as a wedding gift and thought I'd share the original.
(Any 2 1/2" Hole Saw will work, but wanted to provide a picture.)
The cutout is large enough to hold either model of the Anova, but the original fits nice and tight and the mount goes right over the lip of the cooler. The Bluetooth model can turn freely in the hole and doesn't need the mount at all because the lip towards the top of the circulator stops it from falling through. If you're concerned about the circulator turning freely, I'd probably try attaching some velcro to the circulator just below its lip.
I fill the cooler with hot water and it only takes about 15 minutes to get to 140 degrees. I also used Great Stuff to fill the hollow lid a bit, but it's really not necessary. If you decide to do this, make sure the screws are removed from all holes, so air can escape and allow the Great Stuff to fill the lid easier. You'll need to insert the Great Stuff tube at most of the screw holes to ensure you fill as much as possible. Finally, I removed the rear hinges and the interior "holder strap" because you can't really tilt the lid with the circulator mounted.
Sorry about the noisy pictures from my old phone.
We store it under the stairs just like this. If you don't like the circulator sticking out during storage, remove the water diverter to pull the circulator out and the Anova fits nicely inside the cooler.
We store all the accessories inside the cooler:
Here's how nicely the rack fits in the cooler:
Here's how the Anova sits in the lid:
I removed the adjustable tightener from the mount since it simply isn't necessary.
This is the underside of the lid, so you can see how close to the edge the mount is:
Here's the cutout:
I made it like a keyhole so the mount would fit nicely over the cooler's edge. I just used a sharp blade (e.g. drywall knife) to carefully make the notch.