I used to sail a deep woody with a tin rig, and also a self draining woody with a tin rig. In club handicap racing both were competitive against Lasers in light/moderate stuff, though in a blow I'd often experience the sensation you recall of flying past Lasers downwind, then being passed upwind. Frustrating!
I found that once I'd done the basics (ie made sure the sail wasn't completely shot, put on enough kicker, flatten outhaul, pull on downhaul, sit out hard) I could make the boat a lot easier to keep flat upwind - and hence sail quicker - by dumping the forestay so the rig came aft. This of course assumes you have an adjustable forestay, and if you're built anything like me you'll probably have to do this for every tack otherwise you'll struggle to get underneath the boom. I think there used to be a video on this site showing how it's done by the good guys, but even at my level it made a heck of a difference.
