a bit of an fast, unstructured reply, but I wanted to give some comments
the smallest installation of an Mk 26 was in DG/AEGIS. a lot smaller then kidds and spruances, but not as small as an perry. the main requirement what you need is hull depth, but that goes for the Mk 13 size weapons as well. you just need an careful design, as the Mk 26 is quite blocky and wide, so you cannot put it too far forward or aft.
btw, check your numbers in the first post. I had to read trough 3 times before I got what you meant with Mk 29, SPG-52, SPS 48 and SPS 52 (I still don't know the last 2, as you have none of those radars on your drawing, you have an SPS-49 on board)
without an 3D radar, your missiles will just have self defence capability. in that essence, Tartar/SM-1 is not that much more capable then NSSM (which is the reason no USN ships ever carried that combination) on the other hand, you have a lot of duplicate systems (2 shafts AND auxilary thrusters, fixed and rotating Mk 32 tubes, 2 eggs etc.)
I would really seek rearrangement of your funnel, masts and radars, because right now you really have the disadvantages of the current setup.
your cooling water inlets are not close to your funnel (which is most likely your engine room) if your engine room is near those inlets, the stabiliser penetrates it.
I really doubt about the workability of the new GMLS. note that the Mk 13 fired the same speed as the Mk 11 on 2 arms with her single arm, because the loading was a lot less complex and for that faster. making an reliable, fast launcher would get you near Mk 26 (you could go a bit smaller in length of the arms and the magazine if you do not fit ASROC) but without separate magazines for both arms you are not going to get it working as you would like.