The thing about the glasses is that they were originally part of a larger persona. Clark didn't just wear glasses, he slumped his shoulders, changed the tenor of his voice, and adopted a meek and mild mannered persona. His personality was the exact opposite of Superman's. That was on purpose. To throw people off. The glasses are the only aspect of that persona that they've still kept. The best example of this is All Star Superman. Grant Morrison gets it. He didn't just wear glasses, he made himself look like a fat shlub with bad hair. That's the irony of the Byrne reboot. By making Clark Kent the "REAL" persona and Superman a character he plays, they made him even easier to spot. If all Clark is is "Superman with glasses" then, yeah, he's gonna get spotted fairly quickly. George Clooney with glasses doesn't look like a different person. He looks like George Clooney with glasses. You take the most famous man in the world and put glasses on him, he's gonna stand out like a sore thumb.
If Clark has the same build, facial features and voice as Superman, people are going to notice. Shuster and Seigel never intended Clark to be a real person, he was always a disguise for Superman. Very few versions post-Crisis have understood this. Birthright did. ASS did. To some degree, Christopher Reeve did. George Reeve just came across as Superman in a suit. Dean Cain didn't even try. That was the joke. Superman is standing next to Lois in a glasses and she can't even see him. Compare this to someone like Green Arrow who had a beard that nobody has worn since the 15th century even in his "secret identity". Mike Grell made fun of this in his run with "it's supposed to be a secret?" jokes. This is why I like the idea of super-hero masks having those white eyes be part of their mask. It makes it easier to hide. Batman seems like the only one who could pull it off since his covers most of his face. And only if Bruce Wayne doesn't have a particular obvious chin.
One of the solutions I came up with was what if he has low level telepathy? This allows him to throw people off mentally so they don't make too big a distinction. And even then, it would only really need to be around the Planet staff since they know both him and Superman. It can be connected to the same telekinetic field that allows him to fly.