I worked on the sports question some time ago, so my current suggestions:
Crux sport
1. Patibulum racing
2. Patibulum relay race
No comment needed, distance derived naturally from historical facts.
3. female/vag crux
4. female/anal crux
5. male/anal crux
Athlete lifts himself up on the cross, like ring sport, he/she lowers herself on the cornu, when it is completely in, decided by juror and seen on TV, time is measured. Then the cornu is removed, the athlete holds himself up (no nails, no robes) till he must relieve himself. Time is again measured, and the two times are calculated together to determine the winner.
6. female/male crux
Same rules as before, when the cornu is in the female the male climbs on the cross to enter vaginally, then time is taken, and then again the endurance time of both is taken and the mean of it comes to the comparison.
7. male/male crux
8. male/female crux
Here the crucified serves as second cornu.
We need the time to calculate the winner: There are 2 times: From jumping to the cross till the complete entry of the cornu T1 (seconds) and there endurance time T2 for hanging on the cross in minutes. It had to be tested, but I think
T = T2-T1 gaves a good measure, and largest T naturally wins.
Some of it can be softened and I guess our prude society is not yet ready for my sport events, but time will come ;-)
We've already the Logo for the sports event.