I'm highly sympathetic to the intuition that the liar sentence is devoid of meaning in some important respect, but I don't think we can just declare the liar sentence meaningless and then call it a day. Because in another respect, it definitely seems meaningful. I understand what a sentence is, and I feel like I understand what it is for a sentence to be true or false. If someone wrote on a blackboard "The thing written on the blackboard of room 428 is false," I feel like I would understand what this is saying before I went to check out room 428. Hence I must understand the sentence if it turns out that we're in room 428 already.

Also consider the Strengthened Liar: "This sentence is not true." According to your solution, that sentence should also be dismissed as meaningless, right? But surely meaningless sentences a fortiori aren't true. But that's precisely what the sentence asserts, hence it is true.