you can only do 1-2 of the dailies (the kill 50 and some of the others are super easy) and skip the digging up shinies, since digging up 36 shinies will take you a long, long time. you will still hit revered within 7-15 days, and unless you are an achievement nut no real reason to grind out to exalted.

fwiw i've been revered for 5+ months on 6 chars and have had 0... yes zero mounts drop. tons of everything else including a proto-drake pet on every toon, but not a single mount I HATE THIS EGG