I have gone through this with our train (San Diego trolley). The stairs on our trolleys were steep and narrow. I just dealt with it, then altered my work schedule so I could ride the 20 miles each way instead of using the trolley. They have since replaced many of the trolley cars with flat ones, and the trolley is a good option, but I am now used to and embracing doing the full ride and also like saving the ticket cost. The trolley is now my "back-up plan" in case of emergency/lazyness.
Question: Do you mean that by having two bikes you would put the first bike in a locker at the first train station, and therefore that solves your problem of lifting it on/off the train?
That seems like a pretty good solution until the new train station is finished.
If that is not what you are saying, or if that won't work, I have a some thoughts on how you might make your commute easily doable:
If the folding bike works for you and makes it much easier to do the commute, $150 is a bargain, especially if that would mean one less car.
If you could alter your work hours, or just leave earlier, you could possibly ride to the "more city" train stop when there is less traffic. A good set of lights will be needed if it is still dark. Even if you leave at the time you usually do, have you tried it to see how bad it is? Maybe there is an alternate route on side streets that take you away from the major traffic?
Or, just resign to keep driving to the train station until the new station is complete.