Before being discontinued, Cascade Plastic Booster worked well at removing red/orange stains from plastic items in the dishwasher.  Instructions were to add 3 tablespoons directly into the dishwasher for the prewash and add regular detergent into the dispenser for the main wash.  Apparently the staining occurs when plastic items are washed in the dishwasher along with things like tomato residues, which become embedded in plastic items.

The active ingredient in Cascade Plastic Booster was benzoyl peroxide with a concentration of something like 5%.  It breaks down the lycopene.  Benzoyl peroxide is widely available for purchase online and in pharmacies as it is used in acne medications.  I bought a tube of acne cream containing 10% benzoyl peroxide and gave it a try by squeezing a couple of tablespoons in for the prewash.  I used the Intensive cycle which has a 15-minute heated prewash.  There was lots of foam produced.  I probably could have used less.  But it worked!  It might work even better if used during the main wash and then the cycle repeated with detergent.

The results:

Before washing, the 3 chopping boards were equally as stained.  I only washed two for comparison with the other one.  Not completely white, but not bad at all.

The 3 containers emerged with all stains completely removed!

I've never tried putting them out in the sun.  But after reading your post, the untreated chopping board is now sunbathing outside.  Let's see what happens!

My cousin said she adds 1/2 a scoop of Oxi-clean to the dishwasher to remove these stains.  The only Oxi I have ever used suds too much.  I did buy some Oxi-clean dishwasher detergent.  I didn't notice any difference.

Am I imagining things or didn't Rubbermaid or some such manufacturer advertise a tomato stain-resistant material either during the Olympics or Super Bowl a dozen or so years ago?  I remember a lot of classic Italian grandmas dancing around and swooning in the ad.