From this description I envisage you are designing a faster, better armed version of the Chakri Narubet. Fitted with uprated propulsion and the sensors and CMS of the future frigates but with Mk 57 VLS along the starboard edge of the flight deck. Unsure how many cells you would have with this layout, but any reduction in numbers will be compensated for by the air wing.
Yes, but I am not wedded to any particular design or concept.
Initial thoughts would be something like Garibaldi but with a pair of 16 cell VLS in place of the Aspide slant launchers fore and aft the island with guns and smaller VLS distributed adjacent to but below the flight deck port and starboard, Mk57 down the starboard side works too. A small but not too small ship able to keep up with our skimmers, but not as big as the JMSDF DDHs.
If there was money and crew for three modified QEs, Americas, or Cavours, fantastic, as larger hulls are more flexible and capable as well as deliver better value for money, assuming you have the money to acquire and support them without distorting other capabilities too badly. As for the LHDs, even a stretched one, I don't believe people realise just how tight their aviation facilities are, it is for instance a real struggle to fit the required army aviation elements onboard a these were never configured for deployment at sea, purpose design vessel would still be tight but in not having to fit the equivalent of a reinforced Infantry Battlegroup onboard as well would have more space for aviation.
The concept I'm thinking about have been around for decades, the later RN Escort Cruiser concepts for instance. They started out looking similar to the French
Jeanne d'Arc with a Sea Slug forward then evolved to through deck designs with Sea Slug aft and a twin Mk6 4.5" turret on a deckhouse forward of the island, one with Mk13 Tartar forward or the island on the flight deck and various configurations with Seadart. The different designs had from six and up to a dozen large ASW helos (initially Wessex, then Sea King but even a proposed ASW Chinook) or later Harriers. These ships were very much seen as replacements for the RNs war built cruiser fleet and not as carriers, they were desired for their command an control facilities as much or more than their aircraft.
When the RN was to trim down from their five strike carrier (nominal) fleet to a three carrier one the Escort Cruisers were vital, as there were to be five of them replacing two of the strike carriers in proposed surface / ASW groups in the Atlantic, while the CVA01s would be a global / east of Suez force. When Australia went to the UK looking for a steam powered, Tartar armed, helicopter equipped County class destroy derivative, the RN pointed out that three escort cruisers would be ideal for the RAN instead.