And PKTrekGirl, you should try Thrice. Their vocalist can scream and sing, both.
See, now I took your suggestion and went and watched a few of their videos (Artist in the Ambulance, Red Sky, Image of the Invisible). I like them just fine, but I don't consider them metal - to me they sound like the harder end of alt rock on the first two songs, with some punk overtones in the last one (which was also well within my comfort zone already - everything from The Clash to The Pixies to The Ramones to Jane's Addiction I already liked). So I would class them as sitting right on that Alt Rock/Metalcore line.
My favorite bands of all time are bands like Pearl Jam and Alice In Chains...and current bands I kind of like are bands like Breaking Benjamin, Alter Bridge, Filter, QotSA, etc - which are pretty much along the lines of Thrice, from what I can tell. I also like Bullet for My Valentine, which I think is probably closer to death metal than is Thrice (though still a couple of steps removed, I guess). And as I said, I have recently been playing the hell out of The Birthday Massacre...which seems to be sort of a black metal/industrial metal fusion with a singer that is not really either, but who absolutely makes it all work.
Now granted, I have only listened to a few Thrice songs now...but I think Alice in Chains and Bullet are harder than they are. And I see a huge difference between those bands and death metal.
What I'm trying to get to here is something that is closer to death metal. I like Thrice...but that was not a reach for me. I'm trying to get to a place that is a bit of a reach...but not too far, if you know what I mean.

I don't know...maybe Killswitch Engage is that next step away from Bullet for my Valentine....What do you think?