Filling cavity behind loft hatch architrave

I am in the process of replacing a lift up loft hatch with a swing down one, so I can add a proper loft ladder. I needed to remove the architrave around the hatch, and doing so has revealed a pretty wide gap between the ceiling plaster and the timber reveal to the hatch, about 25mm deep or more in some places, and up to 50mm wide. The loft hatch has a flange on it, but not enough to cover all the gap.

How best to fill this gap? Should I try to nail in some more thin strips of timber first to reduce the size of the cavity? Any tips on a suitable filler for deep cavities on the ceiling? Something like easifiller light I thought might be a good idea?

https://www.toolstation.com/soudal-gap-filling-expanding-foam/p15361

Then trim, sand and skim with patching plaster.

Thanks, I have a can of exactly that foam I purchased a few weeks ago for another job. Pretty messy job but gets it done.

Just got I finished last week, pleased with how it turned out. Cheers!