I'm very similar. I actually ditched my driver. I cover the ball with my normal (non driver) swing, so switching between that and hitting up on the ball (with a driver) just ruins my swing consistency. Yes, I could practice both swings, but I am lucky to play a round a week. I too hit a solid 240/250 with my 3 wood. It's boring golf, but try playing skins with your buddies and just pound the fairway consistently. You will score better. Its just a mind wrecker to not go for the "optimal" driver shot when you know you have it in you somewhere. I think of it like laying up on a guarded par 5. You do that 10 times and you probably gain 3 strokes vs. going for it in those 10 holes. Yeah you may have had an eagle putt or two, but you also hit it in a bunker 5 of those 10 times. Same concept on your tee shot. For sprayers, every tee shot is "guarded," and off the planet is always a possibility. Also, if you can hit 240+ with that 3 wood, your approach game from those drives should still be very reasonable. Your 2nd shot is an easier club to hit than the guy who hits his driver 240.
Bottom line, take it out of your bag for a couple rounds and see if you enjoy the game more. See if you score well.