Hi Steve, I'll say up front I've never been on the Spirit, and haven't been to Koper or Korcula. I have been on the Destiny, and been to all the other ports on the old Thomson's Emerald and Calypso.
You can have a very nice time in all those places without going on any trips, except in Piraeus, where you need to get into Athens.
Thomson's trips are quite reasonable compared to other cruise lines, but obviously with 4 the costs will mount, and you might find it cheaper to get a taxi between you. Are all members of the party adults, or are there children? There tends to be more children on Destiny than other ships, so that might be a factor.
In Kotor you will dock right in town, also in ag Nik. Venice a 15 minute walk, then water bus to ST Mark's. Dubrovnik is a short (ish) taxi or bus ride from the dock, same with Corfu, but that's easily walkable, too. Santorini you tender and only need to get the funicular up to town, Argostoli also a tender into town (not a lot there apart from shopping/ cafes). I don't think it's any more expensive to see the sights on E Med itinerary than W Med, in fact in many places you are a lot closer, and the sailing scenery is nicer.
hope this helps a bit, kate