I think the four strong conservatives would not be going for this and would support strict anyway. Roberts will strike down as little as possible of the NYC laws and not support strict scrutiny.
and I think the left four have their mind made up before any aspect of this case was ever considered. The four on the left will vote to reverse Heller totally the moment they get five. if we lose a single one of the five conservative to moderate justices, just one, they NYC will be able to ban muskets on a 50.1% vote o their council and every blue jurisdiction will be able to do whatever they want.
Roberts suggested text/history in Heller orals.