The way to turn compstompers into competitive players is with shoutcasts. Shoutcasts make competitive matches look fun and exciting and interesting, and they provide helpful strategic tips to newer players that make them understand that they, too, can play to win and actually use strategy. Day9 is amazing at this in Starcraft II and things like Tales of Heroes were great at this in CoH.
I think this is the way to go. Some casters do noob shoutcasts every now and then. I think it's a good idea to shoutcast not only the best player but also average and noobish player so compstompers and campaign players can see that you don't have to be a pro player to actually win games and have fun regardless of the outcome.
More mentoring would probably also help.