The fact is, there is no such thing as pure Doom(ok, there is, but in other Doom bands but My Dying Bride). I don't normally agree with Mike on the genres and their necessity, but any band can be judged on how much they have progressive elements, elements of some specific genre and elements outside of its borders. What these borders are and how we find what is progressive and what is not is the main difficulty in our situation.
For example, you say My Dying Bride can be seen as simply just a Doom Metal band. But is Doom Metal something that is the opposite of progressive music? Can't Doom Metal be mixed with progressive elements, much like Death Metal and Black Metal are? For example, is Opeth's Deliverance just Death Metal? Is Emperor's Prometheus album just a typical Black Metal release? I have started a thread, which got deteriorated quickly, in which I developed the idea about each type of Metal being compatible with Prog. Of course, I talked about compatibility, rather than about the existence of some specific Metal genre that is entirely progressive.
Now, back to My Dying Bride. They started as a Doom Metal band, which can be seen on the very first debut album, as well as the Trinity compilation. A doom metal band, with sick, twisted, slow riffs and an obvious death metal influence, with (IMO) elements of Thrash, that they kept throughout their entire career. It is known to the fans of Doom Metal that the sound developed within MDB's music was called 'avant-garde' at the time for its nihilism, experimentation with pianos and violins and nothingarian song structures that transcended metal. However, if you ask me whether I honestly believe that the album is an avant-garde release, I will tell you that whilst it is certainly earth-shattering, it is not 'avant-garde' in the same meaning our site accepts and I consider it my duty to make decisions based on site's specific set of definitions only.
To sum it up, if we shuld make a conclusion on whether MDB are a progressive metal band, I'd like to ignore the fact they recorded As The Flower Withers, as I tend to think only after that things started to get really interesting, intricate, surrealistic and progressive.
Turn Loose The Swans was an album released before the early releases of Cynic, Opeth and Novembre, and defined Progressive Extreme Metal. Before MDB nobody besides certain 80's dark Thrash/1st wave of BM bands, whose progressiveness is not only questionable but from my point of view unlikely, could combine the concepts of beauty and extreme way of expressing emotion as well as MDB did. Turn Loose The Swans not only layed the blueprint for future compositions of bands in the likes of Opeth, but also still remains as a progressive, surrealistic, emotionally intricate and bizarre album up to this day, with violins, keyboards, horns and clean vocals making the essential core of the progressive sound.
I tend to look on The Angel And The Dark River(my favourite) as a continuation of Turn Loose The Swans with all the extreme expression removed and more progressive tendencies added. These two albums were way ahead of their time and I can't see how someone can not see the traits of Prog-Metal in this music. Next was Like Gods Of The Sun, with its watered down, short songs. It is quite a pleasant album, but not one the progressiveness of which I look serious on. The percent album, however, while not being done in a particularly prog-metallish way had more experimentation than ever, with bleak gothic rock songs with influenced from post-rock, avant-garde and even trip hop. As for their other albums, I think they represent the progressive qualities of MDB in the weakest way, although Voivod influenced thrash riffs and keyboards and long compositions with contrast between quiet and extreme can be found there as well. I think their newest album is not too progressive either.
So there, had to make the last paragraph shorter to save me time on talking about less progressive of the band's output.