Something like a geckodrive G251 single axis stepper driver for $89 good to 3.5 amps combined with a NEMA 23 stepper one of the lower current 1.8 amp "long" types $48 on amazon for 340 oz/in torque. That's about $140. That's 68% of budget for 85% of specified torque.
Its easy to find a NEMA 34 with over 600 Oz/in for $60 on amazon but it'll probably draw 6 amps at 600 oz/in and you'll need a more expensive controller. Something like a geckodrive G201X is rated to 7 amps at $127 which just barely makes spec.
The worlds cheapest stepper paired with the worlds fanciest most indestructible controller is probably unrealistic.