wetware: With both dies changed : [ 294 ( = 36 * 7 + 6 * 7, the usual sum of all rolls) + 30 (10 rolls with a 2 changed to 5) + 12 (1 roll with a double 2 changed to a double 5) ] / 36 = 336/36 = 9 1/3. Enough to win most of the long races !

I will leave the "one die" to someone else, but beware, it is higher than halfways between 8 1/6 and 9 1/3.