Wow - thanks for the info - I have a lot of work to do…
Joe
I’ll have to second Ministry. They aren’t really my kind of music, but they fit your criteria.
Faith No More is a pretty good metal band; I kind of like their album Angel Dust and am not much of a metal fan.
I recently picked up James LaBrie’s (Dream Theater vocalist) Elements of Persuasion and it is a pretty dang good cd. The guitarist is damned good, though for some reason his solos kinda leave me flat, and LaBrie is great.
Fates Warning is another great prog band.
Slee
I agree with the OPs sentiment. Tool is the best such band, if they are heavy enough for you.
I’m not normally a heavy metal fan, but there’s a song that I really like by Three Days Grace called The Animal I Have Become. I’m not sure if they are regarded as “heavy metal”, but they sure sound like it to me.
I’m going to second (or third) Dream Theater and Disturbed.
And that’s just sticking to the (primarily) clean-vox’d stuff. I stumbled onto John Chedsey’s Satan Stole My Teddybear at some point back when I was in undergrad. The tastes of the reviewers there generally fit well with my own, and I discovered a whole new world of music through the site. This was also about the same time that The End Records was getting off the ground, I believe, and between the bands on their label and their mailorder, I had my source. They’re still usually my first choice when I need a fix.
I’ve kinda fallen out of touch in the last few years, between a certain amount of drift in my musical tastes and SSMT’s fall into relative neglect, so there’s probably a bunch of stuff I’ve never heard of. Such as this “SunnO” you mention; what’s the word on them?
It’s pretty cool just to find folks who’ve even -heard- of this kind of stuff, much less actually like it. Most of my good friends find my tastes a bit… eccentric, at least. 
I recommend Stonesour - but not the crap they play on the radio. “Bother” and “Through Glass” are painfully annoying to me, but just about every other song on their first CD is great.
It is a mix of heavy metal instrumentals with melodic vocals.
Sytem of a Down is another band that is heavy but doesn’t have the common screaming for vocals. It’s more of an uncommon type of screaming…
Hate metal, love The Misfits. Danzig just has a real nice Orbison twang. (I know the OP must be fully aware of this, but in case anyone else is looking for the same thing…)
Great thread…
I’m Still waiting for Deathlok’s First album to be released… probably too growly for the OP, but then, I wish they would just nuke lyrics alltogether at times… (or make a lyric’s optional version of the CD).
'Nother vote for Sevendust, although some of their ealier stuff is gruff.
Godsmack?
If you dig Sabbath then check out Tony Iommi’s solo album with many guest vocalists including Billy Corgan, Billy Idol, Phil Anselmo, Ian Asturbury and Henry Rollins. Some very interesting work here, not what one would expect.
Also try;
Corrosion of Conformity - Deliverance
Clutch - Blast Tyrant, Robot Hive/Exodus
Sleep - Sleep’s Holy Mountain
Fudge Tunnel - Hate Songs in E Minor, Creep Diets
Helmet - Meantime, Betty, Aftertaste
Melvins - Stoner Witch
I think Dream Theater’s Train of Thought album is an excellent recommendation for the OP. IMO, most of their other music isn’t so heavy, though.
Just had a thought: For some reason, I didn’t mention Devin Townsend. I think I may’ve crossed him off as “Not Heavy Enough,” but sitting here listening to his album Accelerated Evolution, I think perhaps I was a bit hasty. Briefly, he’s another of these mad multi-instrumentalists, rather like Dan Swanö, with pronounced proggish tendencies. He can turn out some heavy music, though, both in his solo work and with (as?) Strapping Young Lad (which has, in fact, been Heavy As A Really Heavy Thing in the past! ;)) I would say that Accelerated Evolution and Biomech are probably the heaviest of his solo discs, except perhaps the most recent one, which I’ve not heard yet. Terria does have the standout track of Earth Day from a heaviness standpoint, though, and is an excellent album all 'round, as is Infinity. Physicist I never got into, but it may be more to someone else’s liking for all I know.
I’m not as familiar with SYL as I’d like to be, so I can’t promise what their vocals are like. All I have here is a sample track (AAA) from Hevy Devy’s website. The vocals aren’t exactly sung, but they’re far from the death/black growls.
I ordered some things through Townsend’s label some years ago, and got a signed Christmas card from Hevy Devy and his wife that year. After that, I figure I owe him the plug, at least.
Sorry for the late reply, that website you mentioned has had me playing around all day long. SunnO))))…(yes, the parenthesis are part of the name) are best described as formless drone metal. Like say if Earth or Sleep had fried their brains huffing cleaning solution and continued to record without a drummer. Some say they’re brilliant, and some say they’re almost too goofy to be believed let alone promoted recording artists. Then again I have records by A.C. and Agoraphobic Nosebleed which are really just a few seconds of violent noise per track. Takes all kinds.
I feel your pain. I’m never allowed to be in charge of the radio. Anytime you feel like talking about heavy music I’m down with you.
I was going to suggest classic Bruce Dickenson era Iron Maiden.
or should I say Iron MAAAAAAAAAAAAAAAAIDen!!!
Not newer stuff, but you may not be familiar with Queensryche (sorry, I don’t know how to do umlauts). Geoff Tate an incredible vocal range and they only ever did one growly song (Damaged).
YMMV as far as heaviness goes.
Type O Negative lead singer Peter Steele has an impressive bass voice and the band combines goth metal with a morbid sense of humor. Well worth checking out.
A bit late to the party, and a lot of good suggestions already listed. I’ve recently went back to some gems and “rediscovered” Metal Church. Specifically Blessing in Disguise. A band, IMO, that should garner a bit more mention from late '80s - early '90s metal fans.
The music itself is great, the lyrics are often beyond just screaming an idea (almost bardic in some cases depending on your mood), and eclectic enough to never mistake one song for another.
Here’s an Amazon link to it with a sampler of the tracks (scroll down a bit). Tracks 1, 4 & 5 should at least be listened to for an idea of the band.
As a personal note, I’d have to list Anthem to the Estranged (#4) as one of the top 5 “metal ballads” of all time. Social commentary, beautiful composition, and a story that lets you know what is really felt by the guy the song gives voice to.
Not that they’re exceptionally heavy, but Candlemass is definitely worth checking out. At the very least, you need to hear “Solitude”.