Your Maverick should be the same as a Mossberg 500 choke tube wise.
The Mossberg "accuchoke" is the same as the Winchester "winchoke", Browning "Invector" and Weatherby choke tubes.
They are rather short (compared to Remington's "Remchoke" or Mossberg 835 "Accumag" chokes).
In flush fit (even with the muzzle) they are for lead shot.
To shoot steel in a M88 or M500 they make "accusteel" choke tubes that run a little longer, extend past the muzzle and lessen stress on the threaded region of the choketube/bbl.
Jackrabbits at distance (never shot one) I'd expect full choke and #4 shot at a minimum. Heck, most guys here run #4 buck on yotes, might be good for jacks too (if we had them- Indiana). At least then you'd have enough oomph for either