This seems like just the thread to jump in on. I JUST ordered Axioms today and my musical diet is probably 95% metal and 5% Frank Zappa and "other."
Given that you're not into growling, and your metal tastes so far seem all "aboveground," I'd recommend the following bands.
Just google their names with myspace, as i think they all have streaming samples.
Pelican (no growling, because they're no singing. good choice given you like Isis)
Electric Wizard (punish the low end of your system
Slough Feg (and earlier listed under the longer "The Lord Weird Slough Feg. )
Hour of 13 (since you like early Ozzy/Sabbath)
Mastery (Instrumental thrash riffing marathons!)
Overkill (earlier, maybe something like Years of Decay or Horrorscope, given your earlier thrash preferences)
Ulver (admittedly not as metal as they once were, but if you want some great stuff to crank up with lots of layers to discover.. pick up their newest: Shadows of the Sun)
Blind Guardian (no growls, quite a few addicting songs. newest one is quite good)
Symphony X (more on the progressive side. tight playing, good riffs, no growls.)
Ark (Get the 'Burn the Sun' album. Catchy slightly progressive songs, fantastic drumming and singing.)
Sir Lord Baltimore (If you liked Zeppelin, try these guys but only the albums "Kingdom Come" and their self-titled, which sell now as a double. Later on, they went soft.)
Wolf. (Their last album "The Black Flame" is pretty fun. Again, lots of catchy songs. Probably closer to hard rock.)
I could do this all night, I also help to produce a small underground metal podcast.
(search for "Shadow Kingdom Radio" in the iTunes store, it's free to subscribe)
We'll see how these treat you first and get to more reccomendations later.