TNHagies
Can not help you to much with the Genesis, but you could e-mail Underclocked, he had one he experimented with a lot - he might be able to help you.
As for the Hawkin, if it is a TC Hawkin - then I would tell you right now you could not go wrong with a 460 grain .503 Bull Shop conical. It is a slip fit conical ( no short starter needed) loads just like a real snug sabot combination. I would also suggest a .125 x .510 shot card under the bullet and on top of the powder... (stops the heat of the T7-3f from melting the bottom of the conical). In my Renegade - I shoot 80 grains of T7-3f and in the GM LRH barrel - I shoot 90 grains.
With these loads I can consistently shoot stationary clay pigeons @ 100 yards... just areally nice shooting bullet and I hate conicals....