You don't need crosses to crucify someone. The most important part of this method is just to have a small, sloping platform to place the feet and a three coils of hemp rope: One for each wrist, the third for the feet.
The exhaustion and asphyxiation stems from the fact that you're having to alternate supports between the shooting pain in your legs from the diagonally down sloping foot support and the constriction of your lungs from being hung by ropes on your arms. Sooner or later, the pain in your legs gets too much and you can't prop yourself up anymore, slowly choking to death. This would usually go on for a day to a day and a half.
The draw to using this method was basically a fatal version of a pillory. The crowd could jeer and toss rotten fruit at the victim over a long period of time. And it gave the public a slow, torturous death to watch and remember what happens to those who would offend the state.
Lastly, when that victim finally passes on, they eliminate. As in, they empty their bowels and bladder as the body shuts down.
So yeah, that's the long and short of it, if you'll pardon the pun. With time sped up, it might be a way to give something rare in Arm: A dramatic death that allows some emotes and speech.
Lastly, to address religious concerns: Christ's crucifixion was unique, involving scourging on the way to Gologtha, as well as a crown of thorns and iron nails. It's iconic, literally speaking, but this execution method existed centuries prior. There's no need to attach sacrilege to what was basically a way of executing non-Roman citizens. Incidentally, Roman citizens were executed by simple beheading. Quick, clean, and merciful. You might say that most arena matches would have a similar view by the populace...
...except sometimes the criminal wins.
