If his mane is fairly thin, you can absolutely use a thinning comb. There's some skill to using a thinning comb and having the mane still look right, I like to draw the comb through the mane at a 45 degree angle, doing very small sections of mane at a time. I have often used an old bottom clipper blade and that works very well too.
Pulling it after a hard work out is a great suggestion.
If you really *have* to pull it in order for it to lay over or braid properly, you've got a couple of options. 1.) Twitch him for the mane pulling. (You'll have to break this up in 15 - 20 minute sections.) 2.) Get a topical anesthetic sprary, either from your vet, or something over the counter like Solarcaine, and spray the heck out of the section of the mane right before you pull. 3.) Sedate him. If you're comfortable doing this yourself, great. A few cc's of ace IV will do the trick, you'll just need to work fast.