On a cocker, you need a large diameter ram and an adjustable Pneumatics reg, otherwise you sacrifice ROF. You do not need a high-flow valve or LP springs (Which improve efficiency, not chopping). STO Ram+ Rock or Tickler does this adequately with some fiddling. Timing isn't the issue, LPR tuning is.
A Matrix with Red Bolt Kit and Trinity already does this, no further mods needed.
Excalibur: Does this when setup according to AKALMP's specs.
Timmy: No frikkin way with current parts availability, theoretically acheivable (Timmy is really modified bushmaster internals in a modified spyder body).
Impulse: Yes with LPR Reg Mod and tuning, may require some valve work.
Bushmaster: yes with tuned LPR or external LPR mod; and vapor mods (LP Springs and high-flow valve).
Shocker: Depends on Bolt & Tuning.
ICD is the big winner as they also sell a blow-forward (Desert Fox?) which the Level 10 could be adapted for.
2k2 VF Cocker, STO/Eclipse Blade, Old-Style 14" Boomstick,
68AutoMag Classic Feed CF11023, Ring trigger.