Cabin floor liner options

[fregata]

Apologies for the convoluted title but I am not sure how to describe this. The cabin sole is teak and holly and while that could probably use some attention, it is not the subject of my inquiry.

Adjacent to the cabin sole are curved portions of the hull that do also occasionally get walked on and they are currently lined with this sort of rubber diamond tread patterned mat. Under the galley stove, under the nav desk, and below the hanging locker. It is delaminating and peeling in regions. Even where it isn’t, it has a habit of collecting filth that is difficult to clean. See the pictures of what I am referring to.

Do people have any good suggestions for what to replace it with? I have considered using a cork sheet of some sort and then finishing it or sealing it somehow. I would be grateful for any other suggestions or experiences people have had. As I don’t know if there is a particular term for these areas I haven’t been able to turn up any specific threads. I would like something durable enough for the wear and tear of foot traffic while not being too slippery and also relatively easy to keep clean. Ideally something easy to install.

[JimsCAL]

My boat in those areas is fiberglass with non-skid textured gel coat, just like the deck. I wonder if a previous owner applied those mats and what is underneath.

[fregata]

From the bits that have peeled away it seems like all that is underneath is the unfinished fiberglass of the hull which is somewhat coarse.

I suppose one possibility would be to sand/fair it smooth and then apply some paint with a non skid additive. However, living aboard in a winter climate I quite like the idea of something with a bit more insulation.