You said you don't like growls and you don't like the cheese. What then, are you doing in the Progressive Metal genre? Below are some bands that take some of those progressive tendencies and make almost exclusively non-cheesy music.
And all these names. Like 'Seventh Wonder', or 'Firestorm'. Then the album title would be something like: 'Keeper of the Seven Keys, Part 1: The Goblin Chronicles'. It just screams unoriginal and pretentious to me.
Lolwut. 95% percent of what I've listened to recently has been very good progressive metal and lacks both growls and what can be perceived as "cheese". I'm not saying there isn't a lot of both in the genre, but I've never once gotten how this can be the perception of the genre by those who don't like it. At least the OP mentioned specifically that it was specifically the Power Metal influences that he wasn't a fan of. I mean, growls I understand, I'm not a fan of growls at all. But it seems like the vast majority of bands don't have them. I get getting tired of the genre after listening to it for a while, but to imply that Prog Metal is unoriginal and pretentious because you don't like... Power Metal-y band names and lyrical content? What further confounds me is that you included Tool, SOAD, and A Perfect Circle (though I understand that the OP may enjoy them). You don't even have to give it a chance and you definitely don't have to like it (not directed at you, more of a general statement), but I wish that when I read criticism directed at the genre, it would be more consistently valid (and it can be, nothing is infallible). It reminds me of people saying they dislike Thrash because of the 80% or so of unknown bands that are really just "Fashion Thrash" bands, still writing Slayer-esque lyrics about killing "posers". Well, if you cared to look, you can find a bunch of truly great Thrash bands that aren't like that at all! Not to mention that these are facets that are not integral to the sound. One common criticism I hear of Prog Metal is that it all sounds the same. Yes, because DT sounds exactly like PoS, who sound just like Prymary, who sound just like Haken
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A lot has been covered so far, but a few more you might like that are lack or just about lack any Power Metal qualities. (for each I scrolled up to see if kirksnosehair had posted them haha):
Akphaezya - Anthology II (got growls, but like Haken's Aquarius, it's probably like 2 minutes of the album in total.)
The Aurora Project - ...Unspoken Words
Clockwork - Surface Tension
Eumeria - Rebel Mind
Explorers Club - Age of Impact (with JP, JLB, Steve Howe, bunch of others)
Frameshift - Unweaving the Rainbow (Honestly, not a big fan of this one save Message from the Mountain and Off the Ground despite JLB's great work on it, but everyone I've shown it to has been the exact opposite, so there's a much higher chance of loving it, it seems)
Jun Senoue - Anything really (Hear me out on this one - Not exactly Prog Metal, but fans of the genre and VGM are sure to appreciate it, and ska-inspired metal riffs + horn section = rad as hell)
Roswell Six - Terra Incognita: Beyond the Horizon (also features JLB and a few other great guests)
Zero Hour - The Towers of Avarice