If the soil is packed that hard, doubt the spring cultivator would do the job.
I own a Danish 'S' tine cultivator. It definitely would not stand the strain. Cultivators are engineered to be tertiary tillage implements.
I own a Rollover Box Blade and have shared your experience with the blunt, angled rippers being hard to pull. Wrong shape for your task, right shape for getting to bottom of road potholes.
I own a Field Cultivator as well. This is the implement you want, or alternatively a Subsoiler, preferably one with a parabolic shape blade. Parabolic shaped rippers pull through the soil with much less draft force resistance than other shapes.
Both my Box Blade and Field Cultivator have five tines. Tines on Field Cultivator are 1/2" wide, tines on Box Blade are 5/8" wide; close to the same.
A PTO powered roto-tiller would be another good choice.
Work your dirt when there is at least some moisture in it.
VIDEO: Tractor Ripper, Field Cultivator, Tillage Tool