I wonder how you manage that, I seriously can't go over the infamy limit to avoid the dog-pilling, not because that's the problem but because then my WE is stuck in the 20s and mass revolts pop up everywhere from both the WE and the infamy, and even if they're all quelled by the (hunting rebels) troops - which they aren't because one in every three provinces suddenly gets stacks of >10 rebels, they still flood my screen with popups and all those troops start draining my manpower and my stacks of 32-16-16 suddenly become that much less efficient if they're fighting like 3-1-6 and just can't reinforce.
Sure, I get it, conquering the world means fighting everyone at the same time including your own people and it must be a slow planned process, but still, how can it ever happen when for every 10 provinces you occupy, you only get to incorporate 4 in your realm and then have 5 years of truce with everyone and their dog that decided to jump in the pool of trying to whack the human player?
I think the others have already identified the big problem in your mega-stacks. That's why your war weariness is in the 20s. When I had 250 infamy, I deliberately kept my stacks small enough that they never had attrition in their base provinces. Every so often it was necessary to assemble a larger army to fight an invasion, but when it was, I reduced it into constituent parts again as soon as the threat was dealt with. Thus, war weariness was always fairly low, often less than 1. It did help that I had pretty capable rulers, particularly in administration. Good, long-lived emperors are a big help. That much lower war weariness meant 20% lower revolt risk, and thus even though it was fairly high due to infamy penalties, it was manageable, and my manpower always stayed in the hundred thousands.
I did double my army from 300,000 to 600,000 after I went over the infamy limit, so my army didn't get swamped by the rebels. Thus, I had a pretty big and expensive army. But it suffered fairly few losses.
I also turned off notification of rebel uprisings and battle results, because there were indeed way too many. Instead I had a lot of armies on automated rebel-hunting patrol, which works pretty well when your armies are sufficiently advanced and sufficiently large (but not too large). And I didn't really try to conquer the world, though I could have. It would have eventually ground to a halt due to the two 15-year periods where no one declared war on me and I couldn't declare war, but I could have conquered more than I did. I just didn't want to anymore.
Overall though, it was less fun when I had 250 infamy than when I had 20. The penalties are indeed penalties, and you do lose a lot of control over what's going on when you're paying tons for a huge army just to keep order. Keeping order becomes 85% of the game, and that's not very fun. And even if you fight a big country, your army is so big (even when leaving some behind for rebel patrol) that it's no contest. Castille/Spain, Austria, and all the minor states could have invaded at once and only forced me to be more careful, without risk of actually stopping me.
So eventually I freed Quebec as a vassal, lost about 100 infamy from that alone, freed some other states, and got my infamy below the limit again. Then the rest of the game ended in relative peace.
Also, this may not have been the best method of dealing with 250 infamy, as it was my first game. But it worked well enough.