Where the deck is perpendicular to the beam, can they provide a fillet weld to the edge of the beam flange and to the deck?
Where the deck is parallel to the beam, have them add a flat plate from the edge of the beam flange and reach over to the next low flute. Provide a butt weld to the beam flange, and fillet weld to the deck.
Wouldn't that lock the deck down to the beams and transfer the diaphragm shear to the beam as well as provide your top flange bracing?
Note: The deck is still somewhat bracing the top beam flange since friction from the deck bearing on the beam is providing some resistance. But we like to ignore friction in the event of vertical seismic loading, but you did mention low seismicity.
There should be a retrofit here that doesn't require tearing things out in this case..is my thought.