I tried some New Londo Ruins co-op and was summoned after a rather long wait. We had no problems with the boss, mirroring my experiences of just steamrolling them that I had in my solo NG, NG+ and NG++ games. I had always defeated them before the next one arrived. I also had yet to die in this fight.
But then I was summoned into a game where they had significantly more health. So much more that the second one would arrive when the first one had half his health left. I died, put down my sign again, was summoned by the same guy again, and died the same way again.
I think I missed the boat in a way. Summoning is probably best done below level 80. I thought this particular boss was a good choice as I (mistakenly as it turned out) thought it was a complete pushover, but I think I need to try somewhere else.
I have some questions. I'm level 125. Should I level up more for more HP and damage output or would this hurt my already poor chances of being summoned? Or would it perhaps make it even more likely that I end up in someone's NG+++++ where victory for a klutz with a shitty build like me is unlikely?
I'm not sure what you're asking. You're SL125, which falls in to the range that most people seem to stop leveling, so you're probably able to be summoned into anything from a regular NG to a NG+x7.
If you were just running through the NG+s by yourself or with a friend you knew would stay in the same level range, it would be a good idea to keep pace with the increased HP and damage of each additional NG+, but like you said, that would also decrease your pool of possible co-op partners.
If you're really doing as well as you can vs the 4 Kings(using either strategy, taking with high poise and just twohanding your strongest weapon, or dodging their attacks and spiking them with pyromancy/sorcery, then you might want to consider starting a new character with a very specific build planned out.
With a good build you could probably beat the 4Kings solo until NG++ or NG+++. Doing it Co-op would probably just make it that much easier.
Maybe post your build and let us see if you made any big mistakes.