For me I've taken it a step farther, Im finishing a 2nd spriest on Alliance side, just cause I wanted to try out the opposite faction on my server, furthermore leveling a 3rd spriest on a pvp server cause I wanted to try out a pvp server (all 3 are the same spec, pvp main spec, pve OS). Honestly I dont find it strange, I truly enjoy playing shadow and ONLY shadow, I have several other 85s but I play shadow because I truly love the spec, and playstyle.
I can understand what you mean by feeling like your gimping it by having to change gear, reforge, regem, re-enchant etc. While it may be easy to play two specs with two gear sets, I fully understand wanting to play to your classes maximum potential and that just will not happen when you have 2 gear sets for essentially 3 specs. THE ONLY way that could work is if you re-gemmed,re-enchanted, re-forged, and re-specced and that can be extremely cost inefficient, I fully agree having another priest with its own gear and etc brings a certain piece of mind. HOWEVER, I advise you to only do this because you REALLY want to play the other spec, and give it the time and dedication it deserves, because many get discouraged that one spec they play does not go as well as their primary and end up abandoning it for their primary.
Unfortunately it is very time consuming for me personally I had to stop on my 2nd and 3rd till I get more time, RL is very time consuming for me especially right now, I barely have time for my 1st priest. If you have the time to dedicate to it, then go ahead and do it.