I've not used a chainmail scrubber, so I don't have an opinion on them yet. I have good success with Lodge's polycarbonate scraper for any stuck bits, and a nylon brush as you recommend. Here's my cleanup process if you're interested.

I just had the opportunity to use this scrub brush a couple days ago and immediately ordered one. It does not have a scraper on the back like the IKEA one you linked to, or the brush I already have, but I use the Lodge scraper anyway, and it has nice sharp edges that have held up well for years. The thing I really like about the Scotch-Brite brush I linked to is the extra stiff thin rows of bristles on the back where a scraper would be. It works really well in tight corners like the lip around the edge of my Dutch oven covers.