Without digging through data sheets, and going off a fading memory, I believe that ex cov is only for flat (<2:12) ceilings. As such, ex cov is not in order. It seems like you may be stuck with std cov sprinklers. As far as the concealed space, you may be able to get it with a single row of Tyco BB1 sprinklers.
If it is 22' wide, I am assuming the trusses span the 22' dimension. Therefore, you would only need 2 branch lines at 11' apart (66" from each end). You would then put 3 sprinklers on each branch line for the 32' dimension. So, you only have 2 branch lines. If you can hit the concealed space with the BB1 sprinklers, you have cut it down to a total of 3 lines for everything. Again, verify before taking any of this to mean anything.
Assuming that this is subject to freezing, you should be small enough to go with a small anti-freeze system vs dry system. Most of the contractors in the areas I deal with prefer to have a small area like this as antifreeze instead of a dry system. (based on a previous thread, if the AF piping is >40 gal, make sure to do calculations using Darcy method instead of Hazen)
I hope this makes sense.
Travis Mack
MFP Design, LLC