I'm looking for bands that sound like:
Queensryche (First 4 albums)
Lethal
Toxik
Fates Warning (First 3 Albums)

I'm already aware of Realm and Watchtower so need to include those, but I'm trying to find other bands that sound similar to what those bands were going for, in terms of style, vocal quality, and the overall feel of the music.

Oracle/Prodigy's As Darkness Reigns definitely falls into the same vein.

There are loads and loads of Queensryche clones. Screamer, Dead Calm, Mercury Rising, and Syrus are a few of the better ones in that category.

As for Fates Warning, while the imitators aren't as numerous, they tend to be a lot better. Check out Enchanter, Cauldron Born, Chozzen Phate, False Witness, and early Steel Prophet.

If you're just looking for quality power/prog, check out Adramelch, Laissez Faire, and Crimson Glory.

False Witness, Chozzen Phate, Enchanter, and Prodigy are all extremely sick!! Any other bands like those?

I'd say Cauldron Born's debut is pretty close to those, but it took me a long time to get into. If you don't like it now, give it some more time.

Chozzen Phate in particular sounds pretty similar to Psychotic Waltz. You may have heard them already, but if you haven't done so yet, check out their debut. You also might like Slauter Xstroyes, they're pretty technical and strange but they have a lot of charm.

Unfortunately, there's just not much else out there in this vein. I will give you a few other bands, but all of them have some significant drawbacks. Sage Meridien is some kickass music but the vocalist can be hard to tolerate. Then you have Apostle, Recon, Sacred Warrior, and Scarlet Rayne, which are all quite good musically, but their lyrics are uber-Christian. I personally can't listen to them, but if you don't mind the lyrics, check them out.