A Largeish Electrolytic Capacitor (watch the polarity and voltage rating) connected to the +12v where it enters the PSU would de-couple the supply a bit and act as an energy store and might help; but it wont affect voltage dropped across connections and wiring. It might be worth trying though. Fully charged batteries might be as high as 14v for a while, so two in series would be 28v, a long wire might bring it down a bit at the PSU end. Can't you connect the LCD to the PSU output and run it off two batteries in series, and run the scope off 12v? It should still run for a while, I would think. It would be helpful to know just how much current everything is pulling.