Bill,
Have you considered providing short bridging members between the two beams: to create a kind of ladder, or otherwise similar to battened column. The displacement of one beam then becomes tied to the displacement of the other and the effective length for lateral buckling is reduced. Could still use plywood top and bottom for the bridging/bracing it just doesn’t have to be continuous box section: unless have an aesthetic reason.
Regards
B.Tech (mfg & mech), MIIE, gradTIEAust
mailto:sch.tectonic@bigpond.com