I've been to Iceland twice on land trips, have done DCL and cruised the Med on MSC - because DCL was just too darn expensive for a port intensive cruise.
If you really want to see Iceland, do a land trip. Your statement there says it all. I loved our DCL cruises, but for the Med, we went concierge with MSC and still saved over half what non-concierge was with DCL. That gave us enough money left over to do a week in France, arranged by a travel company so I didn't have to do all the planning even. Perfect! You could do the same - find a non-Iceland northern Europe cruise and plan a land trip to Iceland on the way there. IcelandAir lets you do up to a 7 day stop over on one of your legs of the trip. It will help with jet lag, since it's only 5 hours from the east coast (bonus.) You could do the entire ring road in 7 days, or spend it in a few places in the west and south if you wanted to be a little more relaxed.
Driving would be easy. There are very few roads in Iceland, so hard to get lost, particularly once you leave Reykjavik, which you really, really need to do. Reykjavik is a nice city, but the draw of Iceland is it's amazing scenery. Planning for next year, you still have LOTS of time to find lodging to your taste and budget. Iceland is expensive, because it's an island with few natural resources, but you can cut costs by self driving, self catering at airBNB's, and enjoying the scenery is free. I'd splurge on specific activities - zodiac boats in Jokulsarlon glacier lagoon, an Into the Volcano tour, and snorkeling at Silfra. I would LOVE LOVE to get out to the Westman islands and the westfjords.
The major sites near Reykjavik are "crowded" for Iceland, but once you get out of that part of the country, it's better. And with the long days, and your own car, you can see the sites very early or very late and avoid almost all people.