Yeah, get one of those cleaning brushes. Cut the handle off the brush and secure the wire part that was attached to the handle into a cordless drill. You can clean the hell out of some fittings this way. FAST and it does a good job. For a quick, easy cleanup, use muriatic acid about 50/50 water and acid. Soak your fittings. They'll look like new. But the acid takes the coating off the fitting, so they will re-tarnish faster if they've been dunked in muriatic acid.
As for older fittings not heating up as fast, first, you might want to use acetylene or mapp gas instead of propane. Second, if you have some real old fittings, the older fittings were cast using thicker material so they will naturally take more time to heat up. Third, if the fitting is dirty (more than tarnish), dirt will also pull heat from the copper.