I noticed you used the term ἐσταυρωμένον and this is the term used in my Interlinear, but on further study, I discovered it was originally stauroo 4717 from stauros 4716 only the latest Strong's expanded red-letter edition gives this. Stauroo means to be impaled upon a pale.
I used the word e'stauromenon because that was the word in the verse I was looking at, 1 Corinthians 2:2.
"For I decided to know nothing among you except Jesus Christ and him crucified". ESV
I didn't want to use the word "crucified" out of respect for your beliefs, since the word "crucified" is derived from "cross". The term Stauroo doesn't specify the shape of the stake, and it also means to crucify. Strong's says "see stauros", which I did. Stauros is from the base of histemi, a stake or post (as set upright). Histemi is a common Greek word and it means to stand, or to make to stand. Either a cross or a stake stands up or makes to stand, so the word Stauroo isn't evidence of whether the standing beam had (or didn't have) a cross beam.
I felt that e'stauromenon was a more generic term for the murder of Jesus Christ, whether on a stake or a cross. I just don't think that there is enough evidence in the scriptures to insist on any one particular shape of the wood. Perhaps a look at other Roman executions from that time period would help?
I'm not agreeing with you, and I'm also not disagreeing with you. I just feel that Jesus Christ and His death for us is much more important than the particular shape of the death instrument. His death was the payment for the wages of sin which we owe and as you probably know, that concept is very important to me. "For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord".