If you start in LA, getting a ride out of the urban area before you start is an excellent idea.
If you only have 7 weeks to do this, you're going to need an efficient route. The shortest route Google can find between LA and Ocean City is 2773 miles, which doesn't sound too bad, only requiring about 55 miles a day for 50 days (with no rest days). Unfortunately, this route is completely unsuitable for bicycle travel. If I add the "Avoid highways" option to Google maps, the route goes up to 2982 miles, or 60 miles a day, but it provides a possible route.
If you follow ACA routes, it typically adds about 50% to the distance you might come up with otherwise. Unless you're prepared to do a lot of 100-mile days, that might be more than you can afford.
Decide how many miles you think you can do in a day. Figure out how many days you have available. That will give you the maximum length route you can handle. For me, I average about 5 miles per day above the route mileage for seeking out food and a place to sleep, so figure that in. If the ACA Pacific Coast route plus the Western Express plus the TransAm plus the hop-off a the end is within your distance range, then I'd recommend that. Otherwise, take a look at the Google "Avoid Highways" route and customize as you see fit.
Are you camping? Cooking? Are you a light packer, a medium packer or a heavy packer? Is money tight, or a bit flexible? Are you going to start out in top shape? How many miles do you think you can do a day?