I don’t see any reason he can’t be fixed, given that Indian characters appear on other comedies without the problems that I understand are detailed in the book. AFAIK, people don’t mimic the Big Bang Theory guy.
I admit I don’t know what would fix it, due to not fully understanding the problem and not having read the book. And not having watched the show. But one idea would to just actually address the whole thing in-universe. Create the real life problem by there be someone on TV who is a much worse stereotype, and have it follow Apu and other South Asians and see how it affects them. Hell, make that person Homer, since being the idiot is kinda his role on the show. Hell, don’t end it happy: have Apu wind up leaving for a while. Because, even if you fix the problem, it doesn’t take away the hurt.
Do it right, and I think people would see the intent, and not freak out about Apu leaving. Though maybe leave some sort of note about him saying he’ll come back, and have a joke about whether he’ll be the same Apu they know. And then, when he comes back, you have the new voice actor. He tries his old job, maybe, but it’s just not the same, and he moves on to doing something else, while still being around, just showing up like any other character, rather than to fit the stereotype.
At least, that’s my idea with maybe 20 minutes thought.