I can’t help you exactly here, but could you maybe drill some holes in the edges and ziptie something on top, perhaps a grass mat? Otherwise, maybe use some rabbit safe glue to glue some lolly sticks for traction?

Really like that idea LEL! Oakley’s Mama, you have Bunnings in NZ right? The have these seagrass door mats for $1. 

Or you could use seagrass or bamboo placemats perhaps.

The seagrass mats from bunnings are treated with methyl bromide, which is a fumigation process. To quote an article on a bird page

“a) Methyl Bromide dissipates very quickly into the atmosphere – i.e. the most dangerous time to be near it is directly after fumigation. In other words anything hit with it under a fumigation tent ‘outgasses’ the remaining contaminant within HOURS [Dumas and Bond, 1977].
b) Though a very small percentage of residue may remain on the item, Methyl Bromide is highly soluble in water. In fact, the fact that rope items and mats are very dry makes them less likely to actually absorb and retain Methyl Bromide. [page 4 General Fact sheet on Methyl Bromide written for the National Pesticide Information Centre states under the header ‘What happens to methyl bromide in the environment?’: ‘Methyl bromide is broken down by sunlight and chemical reactions in the air. It is also broken down by water and microorganisms.’]
c) I recommend people do what I do – I wash all mats, seagrass rope and sisal rope I use for toys first – by using the following:
To a bucket of hot water, I add approx 20ml mild dish soap [I use a ‘green’ non-phosphate soap, but items can be washed without detergent if that is your preference), and 1 cup organic apple cider vinegar. Items are immersed, soaked and the water agitated. I tip the water out and rinse again, and then leave the items out in full sun to dry.”

I wash my mats in hot water with a bit of white vinegar added, I leave to soak, and rinse, then air dry in the sun. What little residue may have been on the mats prior is no longer an issue after that point.

Wow thanks Azerane, that is great info!
I’ll pick up one of those mats next time at bunnings. And i’ll start treating any rope and string I use for toys as you do.