Just a fly in your face idea, but I'm wondering if you could add a booster pump externally that would only operate intermittently, like at 3/4 throttle or better that way, the scavenge pump would still be able to clear the sump below 3/4 throttle as I'm sure the scavenge pump has to be rated at more flow than the pressure pump. That just stands to reason, but then, is Triumph always reasonable? You are running a PTO for your supercharger and with an adapter plate between the oil filter and the base, you'd be able to increase the flow at least to the point that the internal pipes and drill ways would be the upper limit. You could use either the PTO drive or an electric pump, the electric pump being the simpler to control alternative and a lot easier than splitting the cases to get to the scavenge pump (which you have to do to extract it).
Just an idea and probably the simplest way.