Fascists exist at the extreme corner of the lower right. It’s really impossible to be a 100% perfect Fascist, just like it’s impossible to be a 100% pure Objectivist or Hippie Libertarian or Communist. Those are theoretical endpoints, not practical ones.
So in the context of where Conservatives fall within the quadrant, the question becomes how one wants Conservative values propagated through society. Either through societal mechanisms (shaming, for instance), or government mandate. The former puts one in the upper right quadrant, the latter in the lower right.
Of course, even the two dimensional construct is too simplistic, because in reality it comes down to specific issues (and is therefore really three dimensional)
For instance, someone can simultaneously hold the upper right Libertarisn view that the government should stay the heck out of restricting gun ownership as well as the lower right one that the government should be very much involved in restricting abortion ...
My problem with your box of ideology is that the quadrants are biased.
It is Libertarian-centric. The libertarian labels are neutral and gullible, whereas the conservative ideology is without a true quadrant. Fascist is an epithet.
It would be like a conservative making the quadrants: Reagan conservative, establishment conservative, conservative/libertarian, anarchist.