With the temperature in your part of the world I'd wait at least a week.
You may want to thin the dealer's paint with
automotive lacquer thinner and with a fine artists brush (darn fine) go over the scratch several more times. Apply paint in one direction only. Do not go over wet paint. I'd allow at least a half an hour between coats. I'm quite sure that you paint shrunk over night.
Are you working in a heated garage? If not "cool your jets" until it warms up.
Be darn careful with the wetsanding. Personally I sand very lightly with fine grit paper even if it takes longer. (2000 grit)
Check out this link. It's my "go to" site that I check every time before I ever get out my brush.
How-To Repair Paint Chips & Deep Scratches
If you feel that the paint is not laying in the scratch very well. You can remove it with the automotive lacquer thinner before you start sanding. Then reapply it.
I don't know about the pads. I use a Meguiar's polish pad for about everything.
Again, good luck. If I were you, I'd wait for a few others to chime in. That is a darn big scratch you are working with. Might as well get all the advice you can. It's very easy to "mess up" this process. Not a "scare tactic", just "truth". I've been doing touch-ups for over 50 years. Some turned out well, others didn't.
I am very serious. I have taken weeks to complete a scratch or rock chip repair.
Tom