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 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.