raptor,
You mention the "allen head screws break that hold the drive gear on the lobe". Are you talking about screws that hold the timing gear to the two-lobed rotor in the rootes type scavenge sections? As for the pressure pump elements, I believe Dailey uses steel gears.
There's a couple things you should check. First, I would recommend putting a match drilled and press fit shear pin through each scavenge rotor and its timing gear, if there is not already one present. Screws are no good for taking shear if there is any clearance.
Second, I would make sure that you have enough open space past each main web area in the crankcase to allow air to easily flow back and forth as each pair of pistons pumps up and down. That will minimize the variations in pressure the scavenge pump sections see, and thus minimize the torque spikes on the scavenge rotor attachments.
If what you truly have is some torsional dynamic issue, then you are going about fixing the problem correctly. You are studying the data before coming to a conclusion. Unfortunately, diagnosing and correcting a torsional vibration problem usually involves lots of complex analysis followed by lots of tedious testing to validate your analysis.
If your pump is breaking due to a coupled torsional mode that is being excited by something in the cam drive, you'll have to figure out how to modify your pump's torsional dynamic characteristics to move that particular mode up or down in frequency so that it is out of range of the cam drive's exciting frequency.
If you have the time and patience, try machining one of the parts in the pump drive to make it slightly less stiff in torsion. This small reduction in torsional stiffness will lower the troublesome frequency, and may be enough to move it out of the critical range where it is coupling with the cam drive.
Shaft dynamic issues can be a nasty problem to solve. I've seen these type of problems cause endless headaches even for very bright engineers.
Good luck.
Terry