Always nice to run into another Dick fan, and you mentioned some of my other favorite authors, too (Ellison, Constantine, Clark, and Zelazny). I'm going to enjoy making these recommendations, as you have very good taste in the genre.
First, if you haven't already, check out A Game of Thrones by George R.R. Martin. He's fantasy with an edge to it, gritty, dark, and very original. He has no qualms about ending things on an unsettling note or killing off key characters. Each chapter is narrated by a different character, giving the whole thing a multi-dimensional effect. There are no good guys, no bad guys, but plenty of character-driven drama. I normally warn about adult themes (including repeated mentioning of incest), but if you've read Constantine's work, you should be just fine. This is definitely a great fantasy series to check out.
Idlewild by Nick Sagan. You should enjoy this one. It's very William Gibson meets Philip K. Dick, and while it was definitely influenced by movies like The Matrix and even Roger Zelazny's Amber Chronicles, it has a lot of original thoughts. It's also well written, character-driven, and compelling. Nothing's what it seems, and that's all I really want to say without giving away any details or plot twists. Good book, though, and you should definitely check it out.
Warchild by Karin Lowachee. I can never recommend this book highly enough. Hands down it's one of my favorite SF books after Dick's work. I normally don't like much space opera, but this one book is so unique, so fascinating, I couldn't help but read it all in one go, it was so engrossing. Lowachee plays with point of view and narration, and the voice of her narrator is haunting and chilling at times. It's full of humanity and realism, which is hard to capture in the genre. There are also plenty of parallels you can draw to our current political situation over in the Middle East. If you like dark, gritty, and unsettling SF, you should definitely check this book out, and it's the first in what's turning out to be a very good series.
Nightwatch by Sergei Lukyanenko: If you like Meiville, you'll definitely love Lukyanenko. His books are just now being translated into English, but he's already a sensation in Russia. Nightwatch is the first book in the trilogy, with the sequel Daywatch just released last month. It introduces us to a modern Moscow inhabited by the Others: magicians, shapeshifters, and the mention of vampires (just a mention, though, they don't really factor into the plot). Lukyanenko's work is so fascinating because even though his characters are supposed to be strictly divided into Light and Dark, you see "good" characters committing heinous acts of evil in the name of their cause, and vice versa. If Dick wrote fantasy, I think it would be something like this.
Dragon's Winter by Elizabeth A. Lynn. This is one of my favorite fantasy novels. It's lyrical and eloquent, and Lynn gives her fantasy world a sense of depth and history by including myths and legends that her characters relate and believe in. I find her writing very beautiful and her story, while simple, is still quite moving. It's a good change of pace from some of the darker books on this list. The sequel, Dragon's Treasure, is nowhere near as good, though still a decent read.
Good luck finding new reading material!