Since there's no gate at Greenbelt, if you're willing to get up early and have something 'normal-sized' to drive, you can easily find on-street metered parking places like the Nat'l Mall. But I think it's limited to two hours. You can sometimes actually read the big print on the signs from Google Earth Street View, and combine that with the city's parking web site to figure things out.
I stayed a Greenbelt, drove the Tiger (19' C) in early AM on Saturday & Sunday, and was able to tour all the Smithsonians and monuments that I was really interested in. I left about 1 PM each day, no parking tickets.
Jim, "Of course I know how to parallel park. Why, just the other day I came back to find an official note under my wiper. It said 'Parking Fine'."
'06 Tiger CX 'C Minus' on a Silverado 2500HD 4x4, 8.1 & Allison (aka 'Loafer's Glory') www.tigervehicles.com
I would think that any industrial area might be a place for you, but as someone else mentioned your rig comes into play here. Greenbelt, Springfield, College Park are all areas that I know have industrial parks where you could blend in as long as you keep a low profile. Safe is a matter of opinion in some of these areas.