FatesFan,
I've only been checking out more doom stuff over the past ten months, but based on what I've heard, nothing sounds quite like While Heaven Wept. In fact, their previous albums don't sound quite like "Vast Oceans Lachrymose." I would categorize that album as epic progressive metal with doomy lyrics. It's easily one of my favorite albums of 2009.
That said, if you're looking for something (very) vaguely close to that sound, I would reccommend the more melodic and less plodding doom. Abstrakt Algebra comes to mind. It was a short-lived project formed by Leif Edling of Candlemass. Mats Leven sang on it. They're more of a technical power metal band with some doomy tendencies. They only put out a self-titled album, and if you look hard enough, you can snag a copy online.
Another cool album was Memento Mori's "La Danse Macabre." Though most of their albums had Messiah Marcolin on vocals, this particular album featured ex-Tad Morose singer Kristian Andren. Much to the chagrin of the vast majority of doom fans, I much prefer Andren. Mike Wead (King Diamond and Mercyful Fate's old guitarist) was the main songwriter for this band, and he had a knack for making doom very interesting.
If I think of anything else, I'll post it.
Stay metal. Never rust.
Albert