They could employ a SPY-1F radar instead of SPY-1D. It's a much smaller version of the SPY-1D used on Arleigh Burke class destroyers and the F100. Navantia already integrated the SPY-1F on the frigates they built for the Norwegian Navy. I'm surprised those Norwegian Frigates wouldn't be in consideration, actually.
The Norwegian ships are some of the ones mentioned in the article as having been built to lower, “commercial” survivabilty standards. Indeed, from some reports the Norwegian variants deliberately removed some compartmentalization and battle survivabilty for more crew comforts.
Couple of factors.
1. The Norge ships are only designed for 2x8cell Mk41. While that's enough for local area defence, it's a bit light if you want to carry ASROC or cruise.
2. SPY 1F is a 1st gen system, old hasn't been updated, and pretty much an orphan. It's also passive, heavy, power consuming and expensive
correcting all that will take time and money
OTOH, the basic F-100 while bigger (steel is cheap, air is free) is designed for 48 Mk41 cells. And Navantia is already working on a version with a cheaper, more modern, and cheaper active phased array radar system
. CEAMOUNT and CEAFAR-S are already operational and the initial phase 2 ship design is scheduled to be available by the end of the year.