I would reccomend shutting down the water supply and draining it, then pull the cartridge. Shut the water heater supply valve off, then have someone turn the water on and then back off while you watch in the bathroom. Then turn the water heater back on, and have them turn the water on and then back off while you watch again. You should notice the there is considerably more flow with the water heater on, as both sides of the valve are getting fed at that point. If not, you have a restriction in the hot water feed to the valve. Maybe you will even get lucky and this will flush it out.
A word of caution, a tub valve can flow an impressive amount of water without a cartridge in, so make sure that whoever is turning the water on and off can do so quickly, and be prepared to clean up a bit of water on the bathroom floor.