The Oster mane & tail rake will thin it. You push the mane over to the wrong side then drag it through until you have the desired effect. Worked on my old NF mane!
Our driving pony has a very thick mane, and she also hates having it pulled. I do solo comb it, but to be honest its not as effective as pulling it to thin the mane.
Vet sedation once a year followed by pulling so it's on the short/thin side. If you do this at the beginning of the season and keep on top of it with thinning scissors/rake and running your fingers through it roughly when riding/hacking to thin a little it can keep it managable for 6+ months.