No, it's not necessary to change the invisibility spell at all, although it would make it easier is some regards. Instead, I don't start with the idea that an invisible person can't be located, I do that after I see if that person is located or not. The rules suggest that, all things being equal, being invisible isn't proof against location and that the bias tilts pretty strongly to location in many cases. Starting here, I look, and if I cannot justify reasons other than invisibility that an invisibly creature is hidden, I'll assume they aren't hidden. Those reasons might be distance, terrain, weather, having taken the Hide action, etc. If those don't obtain, then I create a fiction that explains why the invisible creature is detectable. By not starting with fiction that assumes things about invisibility or the results, I can use the rules to adjudicate and then describe whatever works. Hence, fiction is both an input and an output, but in different ways and with different expectations. Fiction should only be an input in that it describes the scene -- it should never assume the end results.
As for your last paragraph, I'm the one that initially suggested that circumstances should invoke Page 4 and the GM should make a call -- that the guidance isn't absolute. I also posted an example more complicated but in the same vein as yours here, that points out that a slavish adherence to guidance creates silliness. So, yeah, you're most definitely not talking to me, here.