My D-Pad Is Much Stiffer After I Replaced The Membrane

Both of your theories are plausible and they are easy to separate.

A new membrane will always feel firmer than the worn one it replaced, because what wore out was the rubber's willingness to buckle. That is the fix working. But stiffer than the controller ever felt when new is a different claim, and there are two real causes.

The first is the part. Aftermarket membranes are made to a range of actuation forces and many are deliberately firmer than the factory part, either because firmer rubber lasts longer or simply because the mould is not the original. Unbranded membranes are frequently noticeably stiffer, and that is a characteristic of what you bought rather than a mistake you made. If the part came without a stated actuation force, this is the likely explanation.

The second is seating, which is worth ruling out first because it is free. A membrane that is not fully flat, with a lifted edge, a slightly stretched corner, or a dome not centred over its contacts, needs more force to reach contact and feels stiff and vague. Your detail about diagonals being harder to roll through supports this, because rolling relies on the cross tilting smoothly over domes that are all at the same height, and one proud dome spoils it.

So open it, lift the membrane out and refit it carefully: flat all over, each dome centred on its contact pair, no lifted edge, and the locating features engaged. Also check the D-pad cross sits properly on its pivot and that no part of the membrane is trapped under the cross's edge.

If it is properly seated and still stiff, it is the part. A factory-specification membrane, or a named brand that states its actuation force, will give you the original feel, and it is cheap enough that it is worth buying the right one rather than living with it.