I was going to suggest bleach, but since you have tried it and are not satisfied the only alternative I can think of that "might" work would be to soak them overnight in a hot sink full of water and oxyclean?

I know there are some sort of tablets on the market to add to your dishwasher to remove tomato based stains from plastics. I have not personally used this product, but I digress... It is all that I can think of as an alternative to bleach. You could try using it in the dishwasher with your sink mats, or just put some on them and soak in hot water.

Here is a link that might be useful: Cascade Plastic Booster

I run mine in the dishwasher (wash cycle only), and they come out nice and clean. HOWEVER, they sometimes get a bit whopperjawed by the heat. I put them back in the sink anyway and they eventually smooth out!

I switched to the rubber coated wire racks instead of mats. They fit in the dishwasher for cleaning.Much better than the mats IMO.

I put the stopper in the sink, then liberally shake Comet powder into the sink, run a few inches of very hot water in it and put the sink mats in to soak overnight. My mats are white and very thick Rubbermaid ones and they come out beautiful with some light scrubbing with a long-handled dish-scrubber-type brush.