Bill,
My mentors followed the path you took. However, in housing developments, that theroetica tee "center" usually got pushed closer to the property line, and the course lost desired length. When I started my own practice, I used back tees as the base, moving them out to the mathematically convenient 800 feet/266 yards, which seemed to reflect good players distance from 1984-1994. After that, the best club players went up to about 270-280, and we know where the pros are.
I am currently designing a course where the doglegs are at 850 feet/283 yards. I am putting the next set of tees about 30-40 yards further, basically agreeing with your 240 distance for middle tee players.
There are some mathematical problems with par 5's since, since adding 225-240 yards for the second shot puts the short par 5 greens ahead of the second dogleg. We'll work those out somehow, or go back to 800 feet, back tee yardage, with 20-25 yard splits, plus or minus.
Hope this helps.