I've had quite a few PVC gaming mats printed with pixart printing and have worked out very well.
I got a promo mail from them this morning that intrigued me - nominally these magnetic sheets for printing advertising on so you can stick it to your car/van.
Wonder if you could use it for a magnetic gaming mat though? a 3x3 version looks to come in at a bit over €50 (delivered), so not all that cheap and also my not roll up as well as other materials. Think it could work?
https://www.pixartprinting.eu/wide-format/magnetic-signs-for-vehicles-and-advertising