note that the hull depth of an Mk 22 and an Mk 26 are near the same, as the launchers normally end near the waterline or a deck above it. swapping from Mk 26 to Mk 13/22 size only saves half a deck of height, something easily fixed by designing around it. it is the tonnage of 5000-6000 tons that might be an problem for the application of Mk 26 on this design.
what kind of engine power are you looking for? twin shaft propulsion on gas turbines only means more then just the 2 turbines of the perry, so you will need an bigger exhaust funnel. in addition, the funnel of the perry has purely the exhaust cooling to reduce infrared signature IIRC, the intakes are mostly on the superstructure next to it.
btw, gas turbines are removed for maintenance, meaning you will have to remove your entire mack/mast if your gas turbines are underneath that. to avoid that issue, normally gas turbines are lifted out trough the intakes
something that has issues with using your mack for the intakes as well. and last but not least, the required volume of your mack multiplies by 3 or more, as the air sucked in by gas turbines needs a lot of space, otherwise the turbine pulls a vacuum and stops.
I personally think it would be worth it moving the aft mast aft (you have the space) and go for an proper intake and funnel arrangement.