Do you have any sources on the claim that it wasn’t a cross and was changed later for pagans? The scripture references “coming down” from the cross which to me would imply the one we typically think of.
Also from https://en.m.wikipedia.org/wiki/Impalement,
"I see crosses there, not just of one kind but made differently by different [fabricators]; some individuals suspended their victims with heads inverted toward the ground; some drove a stake (stipes) through their excretory organs/genitals; others stretched out their [victims’] arms on a patibulum [cross bar]; I see racks, I see lashes … "
Sounds like Seneca, a figure from exactly this time period confirms the type of cross we think of.
Another good piece of evidence I just thought of is the oldest known depiction of Jesus: https://en.m.wikipedia.org/wiki/Alexamenos_graffito
It seems the claim might originate with Jehovah’s Witnesses in modern times.