You could just go for plain, pitch-black, un-see-through-able squares. Thracia 776 did it for the first implementation of the series' "Fog of War" mechanic, and though it was
a little extremely annoying, it did what it was supposed to and added a great sense of caution and suspense to an otherwise boring map. You couldn't see terrain at all past the black square "fog", which isn't that bad in practice if you (the map-maker) handle it well and omit as many dead ends from your map as possible. Items that increase your field of vision are precious and useful, though I'm not sure how you'd implement that in a standard RPG game.
I'm getting ahead of myself, though. That's supposed to be fog, not ink or darkness, so the idea is to have things baaarely visible beneath the veil, correct? Well, the problem here is that the dithering method just doesn't work at all for some people (like me) who can't see a thing behind it. Maybe you're right, maybe it is easier to see when things are in motion and you're actually playing the game, but I've seen this dithering-in-lieu-of-opacity thing in a looot of games before (it was really common back before Game Maker supported sprites with an alpha channel), and it just never looks good. It's passable if you're in a high-speed environment (I once made a "toxic clouds" themed level in a Sonic fan game with dithered clouds in the foreground moving against the flow of the level, and it looked pretty good since it was a fast-paced game), but for something slow and exploratory like a standard RPG, it just gets in the way.
If I were designing a map with fog in CUSTOM, I'd pick between either making a gameplay challenge for the player or setting a mood with ambience, and I'd stick entirely to one or the other. For the former, I'd use the black square method I mentioned above; for ambience, I'd just change the palette of the background (and maybe the sprites) to one that mostly appeared milky-white. It wouldn't obscure anything, it'd just be a similar aesthetic to the "dye everything blue" method of making it "night time" in an OHR game.
Long story short, you're not going to get the ideal fog effect you're looking for any time soon with the OHRRPGCE.
(James updated the
Will the OHRRPGCE ever use alpha transparency? page less than three months ago, saying "Eventually, yes, but not soon." So we won't be getting this feature any time in the foreseeable future, from what I can divine.)