As far as I’m aware, it has been stated that there are 2 different “place”s in here: placed from within the map -and- placed from off the map.
The first mention referring to “within the map” and the second mention being “off the map”
If this is all correct, theoretically, could one bring in a Venom Dr. Strange, who brings in a Venom Dr. Strange, who brings in a Venom Dr. Strange, who brings in a Venom Dr. Strange? (As long as nobody was placed from within the map that turn)

(Also you can’t choose lower starting lines, right?)

Venom Strange's power is only checking to see if a character has been placed from off the map, since that's how his power works. Other Venomverse traits are concerned with the other definition of Place.

This is incorrect. Strange is using both definitions of "place". The OP is correct.