Zalman: In case you haven’t noticed there is no halacha necessitating the wearing of a hat and jacket during davening. It is a maila to wear a jacket and hat during sh’mone esrei, the amida, altz kavode before a melech. There is very little else brought down in the s’farim in this regard and for good reason.
I’ve spoken to Rabbonim about this issue and they’ve said that it is plausible to say that just like a tallis is worn instead of a hat for shachris, so to can it be worn instead of a jacket for shachris. Again, they reiterated that “hat and jacket” was a maila, not halacha.
I have personally attended halacha shiurim for many years given by two leading poskim in Flatbush and when this topic was covered in the Mishna B’rura, the above observations were also acknowledged as being held.
Also, if what you are saying is halacha, written in stone, where are the rules in the Shulchan Aruch? We would (and should) not be having this discussion. Is there a special set of rules for those who live in hot climates where jackets are not the minhag to wear during davening? What about before jackets were in existence. Were people not yotze davening?
I know that you would be thrilled to find out that a new halacha seifer (three volumes, over 500 pages each volume) is to be available soon. The first volume deals with hilchos jacket and the next two with hilchos hat.