Wow, thats fantastic that you have a cross with removable patibulum in this "authentic" style, enabling you to re-create the "presumed" real ancient crucifixion method.
May I ask, did you or your "crew" ever try to conduct a crucifixion with fixation of the victim to the crossbeam while on the ground and lifting the victim with the beam on top of the stipes or are you only using it in already fully assembled form?
A couple of things that used to bother me about some of the artists' representations of crucifixion, like this drawing, and the way the timbers joined was that for the mortise and tenon joint they showed the tenon as being a tight fit into the mortise, and they showed it as being just long enough to reach the top side of the patibulum and no more.
I thought a lot about that and about how we, and the Romans, did other timber joinery, what works well and what doesn't. First of all, if the joint is a tight fit, then everything has to be lined up perfectly for the two parts to go together. That might not be easily done under real conditions. What would have worked better is to have the top of the tenon smaller, so that it will go into the mortise easily without the need for perfect alignment.
In the 3D model of a cross I created years ago and have used in a lot of my art, that's what I show - a tapered tenon that makes it quick and easy to assemble with the victim hanging from it. In the picture below from "The Serpent's Eye" you can see the mortise in the patibulum and above it, the tapered tenon that will go into it when it's lifted up.
In the next picture, they have just begun to lift and her feet are about to leave the ground.
Another consideration when lifting it like this is that with the victim's weight all hanging on one side, if they're not careful the beam could turn in their hands. That could break the victim's wrists and they could end up dropping it.
In the picture below, they have the mortise in the patibulum over the top of the tenon, and it's easier to see that it's not a tight fit, so easy to line up.
And then when it's lowered into place on the tapered tenon, it's a tight fit and will get tighter as the victim's struggles make it settle into place.
The other thing I mentioned before is how people have made the assumption that the tenon would only be as long as the depth of the mortise. I've also read articles where the authors said that there was no place to attach a titulus above the head of the victim on a cross like this. But there's no reason that the tenon has to be that short, and it's easier to assemble if it's longer. And making it longer for ease of assembly happens to give a good place to attach a titulus, as shown below.
The subject of this thread is not historical crucifixion, but from what some have posted, it sounds like people have an interest in modeling what they do after what was done by the Romans, up to a point.