Tim,
You are asking the right questions.
Can it be done with carbon beams. In theory, Yes. Practically, no. In order to get them you have to go for a custom production job with probably hand lay-up and the production of a specialize mold. All adds dinero ! I don't know how much it would cost. Your guess is as good as mine.
Bedding compound is allowed in the F16 glass as long as it doesn't glue the beams into place. You must be able to take the beams off and re-attach them without breaking stuff.
Taipan beams are both square and oval. Of course Oval shaped have sort of the same resistance to wiggling as square ones. Having said this I know from a proper comparison that two perfectly round beams resulted in 60 % flexing when compared to two non-circular beams. So this makes a very potent counter argument.
Now I'm sure that in principle non-circular beams are stiffer to circular ones for the reasons you describe HOWEVER its effect may be dwarfed by the results achieved by other approaches like improved beam landing design. The above named example suggests as much
Wouter