I think there is some evidence that the earliest use of crux was a non-fatal punishment rather similar to the British Army practice of tying a soldier to a gun wheel.
Field Punishment Number One - I quote Wikipedia here:-
World War I - British and Commonwealth armies
Field Punishment was introduced in 1881 following the abolition of flogging, and was a common punishment during World War I. A commanding officer could award field punishment for up to 28 days, while a court martial could award it for up to 90 days, either as Field Punishment Number One or Field Punishment Number Two.
Field Punishment Number One, often abbreviated to "F.P. No. 1" or even just "No. 1", consisted of the convicted man being placed in fetters and handcuffs or similar restraints and attached to a fixed object, such as a gun wheel or a fence post, for up to two hours per day. During the early part of World War I, the punishment was often applied with the arms stretched out and the legs tied together, giving rise to the nickname "crucifixion". This was applied for up to three days out of four, up to 21 days total. It was usually applied in field punishment camps set up for this purpose a few miles behind the front line, but when the unit was on the move it would be carried out by the unit itself. It has been alleged that this punishment was sometimes applied within range of enemy fire. During World War I Field Punishment Number One was issued by the British Army on 60,210 occasions.
Conscientious objectors who had been conscripted to the army were treated the same as any other soldier, so when they consistently refused to obey orders they were usually given Field Punishment No. 1. Alfred Evans, who was sent to France where he would be sentenced to death (later commuted) with 34 others claimed that "it was very uncomfortable, but certainly not humiliating". Some conscientious objectors even saw F.P. No. 1 as a badge of honour.
Although the 1914 Manual of Military Law specifically stated that Field Punishment should not be applied in such a way as to cause physical harm, in practice abuses were commonplace. For example, the prisoner would deliberately be placed in stress positions, with his feet not fully touching the ground. The New Zealand conscientious objector Archibald Baxter gave a particularly graphic account of his experience with Field Punishment No. 1 in his autobiography "We Will Not Cease". Baxter's story was dramatised in the 2014 TV movie Field Punishment No 1.
Field Punishment Number One was eventually abolished in 1923.
