Heading east from LA is tough. You don't have too many options on how to get out of California, and none of them are benevolent to the unprepared cyclist. Regardless of which way you, you will have to cross some long, desolate, hot, and dry stretches of desert. You will probably also need to spend some time on the interstate.
One option is to head due east through 29 Palms, into Arizona towards Phoenix, and then begin to angle northward towards to Boulder to pick up the Trans-Am. Another option is to head northeast towards Las Vegas, and then into the beautiful riding of southern Utah, and then pick up the Western Express in eastern Utah or even Montrose, Colorado. One more option is to head north up beautiful 395, and then across Nevada thorough Tonopah and meet the Western Express in Ely. All of these routes can be wonderful and I've done all or large portions of each of them, but I'm having a hard time suggesting one over the others. Regardless, this will probably be the most difficult part of your trip because of the desert environment and lack of services. For turn-by-turn directions, look for a Route 66 guide, or even the Race Across America (RAAM) routes.
At the other end, you can go all the way to the end of the Trans-Am and then pick up the Eastern Seaboard. It's a nice ride and won't add too many extra miles. Personally, I'd be tempted to stay in the Appalachians and follow them north into Pennsylvania, and then head east into New York or New Jersey. Pennsylvania has an excellent set of cross-state bike routes to follow, another resource may be RAAM again since they often end in Atlantic City.
When I tour, I average 80-100 miles on the bike, but take at least one day off a week. Unlike the others, I prefer full days off rather than half days. In the end, we all end up at about the same speed. I find that I ride nearly the same number of miles per day in the mountains as the flats. 30 miles a day commuting should be excellent preparation for your tour. Consider doing a few full day rides on the weekend as your tour nears, and riding with your gear (or weights) so that you get used to the handling of the bike.