Alternatives to adjusting strikeplate height?
Your instincts are right. Bumping out the lower hinge just a bit should raise the lock mechanism a bit and may allow it to properly engage the strikeplate. You also get the risk of messing with well functioning hinges. It may cause the door to self-swing (or even bind at the top or sides).

But the test is easy. Slightly loosen the lower hinge screws on the door. Slip a piece of cardboard or two between the hinge plate and the door. Tighten the screws. If all is well, you can leave the shims or replace them with a thin piece of wooden shim. If it doesn't work or causes other problems, reverse the fix.

If that doesn't solve the problem, you may be able to file down just enough of the lower edge of the strikeplate hole to allow the lock to engage. Newer strikeplates are fairly thin material and can be filed fairly easily.