No power projection? What version are you running?
1.7
And without administrative efficiency or abusing protectorate, how in the world did you stomp the world hard enough to break the uber-coalitions?
By switching up where I was taking provinces. Once I had Shan, Xi, and Zhou as vassals coalitions in south asia didn't really matter, so there was a small one there. Then I just changed where I attacked by watching the culture and religion maps. The south indians didn't care all that much that I was killing the north indians, and no one really cared that I was killing the southeast asians, other than the other southeast asians.
Arabia was a bit harder, so I focused hard on the timurids so I could gain access to north africa (and muslim infantry). That put them and Hedjaz in a coalition. But really, mamluks alone and mamaluks + a 10k army isn't much different. I did have to fight a semi uber coalition of timurids austria and muscovy, but at that point I was nearing a million troops, so I just threw bodies at them till they gave up.
Most of Europe was also in a coalition when I really focused on them. I had all of asia, africa, the americas, and oceania at this point. I was also careful and slowly dismantled Spain and Portugal from the start (GB and France were both protestant, and the iberians were catholic so no alliances there) so realistically the only powers in Europe were GB, France and Scandinavia (which was bloody huge) they would have completed the "Sweden is not overpowered" achievement haha. To deal with them I took advantage of a war between GB and France and took half of France, that put most of Europe and France in a war with me, then I took a chunk out of GB. That put them in a coalition with me, but severely weakened both. Then it was just a matter of dealing with Scandinavia (who was already in the Coalition) so that started the me vs Europe wars. I think Austria had over 1400 AE against me when I annexed them. Haha.
Wait, really? The tooltip just disappears?
Yeah, it does that. I didn't bother with rivals though. I would rival a large power right before I beat them up, got a bunch of power projection for taking provinces and then they would no longer be a choice to rival. I didn't really care, with NF set to military, and tech levels that were on par with the Europeans (and ahead of time usually) the extra 1 to all didn't matter.