It's not the tire dressing, it's the tires. Tire rubber has a product called anitzonant ?sp that helps keep the rubber from drying out/cracking.
As evidenced, I have a 2017 trailer with original tires that (just bought this year) but can guarantee have never had any tire dressing on them. I'm fairly certain the original owner never even actually washed it. It spent 3 years in a pole barn and about a year outside in the sun.
Those tires are bout as brown as any I've ever had. Tried 2 rounds of Bleche White on them and it didn't touch it.
I beleive there are other cleaning products out there that may work better?
degreaser, like purple power or similar. Wet the tire first, spray it on full strength (careful of painted rims), you can literally see the orangey brown stuff running off them almost immediately especially if they're real bad. Let it sit about 30 seconds, hit it with a plastic bristle brush (I use the brush from a broken snow scraper or something similar) and hose off. Leaves the white letters looking whiter than bleche-white ever could (I have never liked the stuff, now with the new formulation it's completely useless), and makes the black rubber look brand new. Doesn't mater how grimy the tire is, it comes out awesome every time. I don't even use tire shine, I'd rather just have a perfectly clean black tire than a greasy looking one.
Just be careful not to let it dry on there, it's really not good for rubber if you leave it on too long, the key is to be quick just to dissolve the nasty sh!t off the outside. You can use simple green too, it's a little less harsh (though it doesn't do quite as good of job as a result)