What would you do in this situation?

So yesterday I went on a few more hours in my Korean game. Difficulty King (it's my 5th game with BNW). Map continents. On my continent there are 5 Civs: Greece, Carthage, Sweden, Spain and me.

I founded 3 cities, going tall with the usual Tradition -> dip in Commerce -> Rationalism, having a decent of growth and culture + a well spread religion with Tithe. I always felt that I had a good science lead but then it happened: I decided that Spain had to go, because of Isabellas HIGHLY annoying missionairies. Originally I planned just to take her capital / Holy Site, so I arranged my army consisting of 3 Artillery (beelined / GS popped dynamite), 2 Lancers and 2 Musketeers and went for the attack. Spain responded - with two Composite Archers and two Warriors. At that point I realized that I do not only have a minor tech advantage over the other civs on my continent.

So now my questions!

What would you do next? With my current military lead, it would be easy to conquer my continent. There are ~10-12 cities left and I plan on starting with Carthage because he snapped one wonder I had only 1 turn left to produce (you might say it's personal). But is it worth conquering everything? And then what, raze those cities? Make them puppets? Is there a disadvantage in puppetering them? Or better keep them around for trading? Sweden build the 5th religion so I thought maybe it wouldn't be the worst choice to eliminate his holy city and dominate the continent with my religion. Maybe I could crush all but one and gift some cities to him, making him a reliable ally?

The other choice would be the completely focus on science and use my advantage to win. But this would be pretty boring I guess and it seems like I miss a chance with my military being so clearly superior at the moment.

Any help is appreciated

I don't see how gifting cities to Sweden would make him a reliable ally. You'd get his vote in Congress if you'd liberated one of his cites but I don't think that's what you're talking about.

If you wipe out 4-5 civs you'll get severe warmonger penalties. You're starting late so I'd imagine you're in danger of the civs on the other continent discovering your misdeeds too. If you're prepared to deal with that then go right ahead, nothing like a bit of war to liven up a game!

If you don't want your cities converted just grab some inquisiters and post them in your cities.

I know, but I did not had enough Faith to buy so many Inquisitors at the moment. Furthermore, I already converted Greece and Carthage to my religion and Spain was messing with that too much. I had to care of Isabella. I warned her.. but she wouldn't listen.

You know, I have a looong Civ 4 background. And my prefered strategy was to wipe my continent clear but keeping one civ on my good side (if that wasn't working as a Vassal). I thought gifting cities will give you a big diplomacy bonus. So if I would wipe out everyone but i.e. Sweden and gift him some useless cities wouldn't he be so happy to be my "ally" for research pacts, trades etc?

Or is the (stupid..) warmonger modifier so high that this wouldn't matter because he would hate me anyway?

Maybe I should just blitz all of them, buy some Frigates and take care of the remaining capitals..

If you enjoy fighting with artillery against composites: Conquer them all.
Otherwise: Congratulations, time for the next difficulty level!

I guess this would be the right time to move up, thanks

I still wonder what would be the correct move to make if i.e. a Civ on the other continent would be equally strong. Just from a "what if" point of view.