Charlie, it's a longer walk back to where you want to be, but if you drive 56th Avenue east from the closed parking lot and cross Tower Road, the next major intersection ahead (stoplight 3 blocks east) is Dunkirk Street. From there you can drive to and park at First Creek Park, a tiny city park patch (kids-outdoors-discovery-zone) west of Dunkirk (the street where the First Creek-Green Valley Ranch hotspot is centered).
To get there:
Turn right onto Dunkirk From 56th and go south to 53rd (just after crossing south over First Creek). Turn right, driving about 2-3 blocks west until the road curves left (and becomes Elmendorf Way). The park is on your right.
Park on the street and walk north through the little park along the sidewalk/path (or meander through the discovery zone habitat).
You'll come out into open fields and new houses on the north side of the creek. Continue to follow the paved path left/west along heavily treed First Creek, and a couple of city blocks ahead, you'll cross through a tunnel underneath Tower Road (still westbound) and enter the eastern edge of First Creek @ DEN Open Space.
The paved path takes you west through the open space, roughly 1 mile-plus, to Buckley Road.
I don't know where the limits of the plague closure are, but the main prairie dog town near the 56th Avenue parking lot is well south of where your path meets Buckley Road -- which is also where you can cross west into the Arsenal on the First Creek Trail . . . that is, assuming the closure doesn't into the refuge as well.
Good birding,
Patrick O'Driscoll
Denver