In reply to the original question:
Since the engineering plans for the DS2 are already in hand, I would save the months or years of design time and simply build another DS2.
If possible I would like the ability to use the constituent beams, that collect to form the superlaser, to individually target capships,
if this functionality cound be included into the design before the construction has advanced to the critical point for alterations in the superlaser design.
This approach would give the Emperor a fully functional, coreworld shield breaching, planet killer
with the full propaganda impact envisioned in the DS1/2 (planet is blown up, not just 'steamed in own ocean'

or melted) in the shortest possible time; and if possible including the ability to get by against capships without an oversized protective cordon of capships.
(I would of course suggest more aggressive use of the onboard fighters then Tarkin employed, and possibly carrier support, but that is tactics, not design.)
The only other DS2 system I would like to have upgraded in a full redesign would be the hyperdrive, to achieve a faster response time against insurrectious worlds, but this is not as important as getting the thing build without years of redesign to include it, and may just be too expensive (cost-ineffective) anyway.