The TL is a nice marker to tinker with. You can source an EKO valve and that should let you drop pressure easily to 600 psi. You may be able to get it down to 400 psi with spring kits.
The Palmer Female stab will go on the grip and let you keep the rest of the setup as is. This is good because it means you will have a lot of volume before the valve to play with. More volume at a lower psi means you have a lot more room to play with the valve. Should be able to get the springs pretty soft to give you a smooth shot.
Do note that every spyder is different, so one spring setup might not work the same way on another spyder, even being the same model. Lowering operating pressure also doesn't mean a smoother shot. Low pressure means you need more volume to flow, which could require a stronger striker spring to make the valve stay open longer.
That's what is fun about spyders though, easy to tinker with, and not difficult to tune but you can do a lot with it.
I like Spyders.
MR1, MR2 LP, EMR5 LP, EM-1, Raven Primal, Victor, Fenix.
Magfed Hurricane with T15 Mags