Hey shorecycler -
It's a little hard to tell what you are really asking, apart from "where can I get a train ride to." You can figure that out by looking at the Amtrak web site. I'd recommend not using the train unless the train itself is appealing to you - it's very slow and not cheap. Flying is best, IMO.
Here's my take on it:
You should probably take some time and consider the weather conditions on the different routes you are thinking about. July and August are much nicer further north or on the coast, rather than riding across the desert or the southern states.
The Pacific Coast is gorgeous, and if you did the whole thing, Canada to Mexico, that would be a great trip, well timed with the weather, and leaving you plenty of time to do it without feeling rushed and get back for the birth. I think the Pacific Coast is absolutely a world-class touring route, probably better than the TransAm.
Or you could do a NJ-OR northern crossing, (northern tier, lewis and clark, or combine with your own route) - you would have enough time if you didn't start out with the southern leg to VA, and it would put you in the northern states where the weather will be nicer that time of year.
Personally I think both of the routes you mention put you too far south for the season.
I can see how having a start/end point at home, riding to or from your door, or using the popular TransAm is appealing, but I think you should "think outside the box" on this one, and see if considering different start/end points might make for overall a more enjoyable trip. Don't solve the problem/expense of the start/end travel at the cost of enjoying the actual trip.