Yep, closed cell foam sleeping mats are perfect to craft your own pads.
They come in several thicknesses. Don't take up mositure. And are (relatively) cheap.
I have cut up a few of those too to create custom inserts for various bags and packs. Use pads to put between things stacked in too-deep compartments in regular photo bags too.
Well worth considering if you want to add some padding to a unpadded bag.
Especially cheap if you buy them at a second hand store, $2-$5ea. around here.
More at a military surplus store $10-$20.
I owned a Billingham once & it was a nice bag but not $200 nice. I know! It's a hobby, spoil yourself.