When moist I can probably push a spade about 3" in.
Here's the plan: I would like to break the clay up as far down as I can, even if its only 6" at a time ~~~ until I can re-pack the track without having spots where there is sand only.
The problem is there are spots 3'x3' of sand only, that the cars dig out. Leaving "holes" in the track surface.
The 3" spade test indicates the track surface is not compacted.
Subsoilers and Chisel Plows are not too separated in function, perhaps overlap in some manufacture's descriptions. Both will get beneath track surface to disrupt deeper, per OP's desire and best pothole elimination practice. In either case, PARABOLIC shaped rippers decrease draft force resistance and strain on the shanks/rippers and would be essential were I making the choice, based on limited information we have. I am sticking with my Chisel Plow recommendation for the moment. I like spring-protected Chisel Plow's ability to reset/trip if encountering a finite hard area or boulder, over shear bolt protection on some subsoilers.
With either a Chisel Plow or Subsoiler the OP can vary the "bite" of the implement by adjusting the Three Point Hitch Top Link.
Chisel Plow will leave the track surface easy to smooth with the grader, while leaving some undisturbed, supportive subsurface after the first pass. Less labor intensive to smooth track surface with a grader, which the OP has, than using a jumping jack. Tractor has a loader if he needs to move material. I speculate OP grades entire track surface after each race.
Chisel Plow should speed rain absorption/drainage as sand and clay is amalgamated over time.
Clay absorbs a lot of sand and remains clay.
Most Chisel Plows are sized for a Category III Three Point Hitch, which I speculate matches the OP's 14,000 pound tractor. Various width Chisel Plows available, with varying census of shanks.
BEAU42X: What is the length and width of your track?
Is track banked or flat?
How many laps is a typical competition?
Are ex-sand holes confined to certain sections of the track or evenly disbursed over the track?
Any problems with standing water after rain?
Correct me if I am interpreting your goals incorrectly.