Just so we're clear, you're speaking of a
paint frame, correct?
I didn't know those existed outside of college theater scene shops. Painting a
scrim "up" just sounds wrong to me, as scrims need to be painted very wet so as not to clog the pores, and I see no way to keep the analine dyes from running down the drop.
Suggestion, paint it "down." Not having much time will be to your benefit, as no one will want it in their way for very long anyhow. In the end it will be faster.