Last year, I decided to do the same thing but did not have good early spring conditions. The cold damp spring caused us to keep the grass tee area closed since the turf was very slow in coming out of dormancy. Conditions were very wet which would have allowed very few days on the tee but I decided this season we would get back to overseeding the tee. .
I sprayed a material in the early fall which should kill some of the early germinating poa annua and allow the ryegrass that we overseeded on the tee to flourish next spring. Of course, we will get some poa annua to probably germinate and invade the area. We seeded 1/2 of the tee that is closest to the parking area which should be enough teeing space for the earlier spring play. I seeded this section of tee that has reduced sunlight and is usually slow to come out of dormancy anyway. I wanted to keep the stronger area of bermuda ready for next spring in case we had an early warm up and it would grow faster and be ready to hit off of sooner if we received above normal conditions.
Overseeding is stressful for bermuda. We attempt to reduce the harm to the bermuda by only drop spreading the ryegrass. My friends to the south who grind their turf down to near nothing when they overseed are beginning to post some nice pictures to twitter regarding reopening or how their rye grass is coming along. Ryegrass can slow bermuda from breaking dormancy because it shades the bermuda and does fight it for nutrients and moisture
So this spring you can look forward to having turf to hit from once the tee is dry enough to allow play.