15 years ago I took a 5th route to Relay Pk - from the lake shore - combined run/hike. From the shore, run up Country Club to the end, go left .1 miles, then right and up Jennifer to the end (7400ft). Pick up the remains of a trail near the bed of 3rd Creek, and start the fun. Climb into the valley a little, then slab up to the left (west) to around 8200 feet at the crest of the ridge - right at treeline. Follow the easy but spectacular ridge to the summit of Rose Knob Peak (9710 with unbelievable views all the way). Hop over the top to the Rim Trail, and follow it to Relay's south ridge. Follow the ridge to the summit. You can run all but the steepest parts...took me 3 hours. Come back either via the road or down the sharp SW ridge of point 9561, but that's sort of brushy. 4500 vertical each way, and one heckuva day trip.
That is a long trip! Notice that one of the routes is from Brockway Summit, and that is almost 30 miles. As for adding your route, I don't think it is necessary to suggest routes longer than 12 miles to Relay Peak as alternate routes. The fact is that there are many ways to hike Relay Peak via long routes. Relay Peak is very accessible because of all the roads and trails around it. For the purposes of this page, I want to focus on the most direct routes. The only reason I mention Brockway Summit is because trail maps provided by the US Forest Service describe the route, and it is the Tahoe Rim Trail section.