After searching around the internet a bit I decided on my game plan for filling the gap. I would buy GreatStuff to fill the large gap and then smooth it all out with some joint compound.
First I vacuumed and cleaned out the gap.
Then I began to fill in the gap. GreatStuff is a product that you can only use one time. If you still have anything left in the container after finishing your project you will have to just throw it away as the foam dries up in the straw applicator and no new foam can come out.
After allowing the foam to cure for a couple of days I used a drywall saw to remove the excess foam.
I can see a few spots where I wish I had filled in with the foam better, but it's too late now!
Then I applied my first coat of joint compound. Doesn't look too promising at this point!
Here it is after sanding, applying a second coat, sanding again, applying a third coat, and....you guessed it, sanding a third time!
It looks acceptable. I then sanded the wall to try and get rid of any small bumps that the textured paint caused. I first tried sandpaper on a sanding block attached to a painter pole. It didn't look or feel like it had done anything. So I went for my palm sander. It feels slightly less textured, but it's hard to tell. My next step will be to prime the entire wall. Hopefully that will make everything nice and smooth so that I can move on to actually painting! Bright yellow wall, here we come!
Filling the Gap, Part 1