Welcome to the cycling community!
How about the getting on the MVT between Fort Hunt and the Alexandria Ave Bridge, where the trail is on the inland side of the GW Parkway? Sounds like you are in that area. North of the Alexandria Ave Bridge, the MVT briefly shares a neighborhood street and then turns back into a multi-use trail. Crossing the GWMP is always exciting because it has become a major commuting route in the area.
The Fairfax County Bike Map should help you plot a route.
http://www.fairfaxcounty.gov/fcdot/bike/bikemap.htm
I’d expect you will find the modest additional distance to get to a safe crossing to be a far better tradeoff than attempting a grade crossing. To help you understand the issues, here is a thread discussing the crossings further north.
http://bikearlingtonforum.com/showthread.php?2354-Another-accident-at-the-GW-Parkway-crossing&highlight=accident+gwmp