Your problem is solar gain vs the mass of your building.
The sun is powerful. A dark, 1 square foot panel that is facing dead square on with the sun, will absorb 90 watts or about 300 BTU/hr from the sun's rays. From the sun's perspective, how big is your roof? I would bet 1000 square feet or more, so 300,000 BTU/hr coming at you. As you probably know, this leads to a dark roof that you can fry an egg on.
Obviously some of that is re-radiated, or cooled by ambient air. But much of it soaks into your home's structure, heating it up significantly - also heating the attic well into triple digit temperatures and thus, heating your ceiling and here's your complaint.
Now if you're wondering about reflectivity of lighter paint colors, I asked my paint supplier about the reflectivity of their 3 lightest paints. 82.6%, 80.7% and 80.4%. All of these are called white. Off-whites head into the 60s real fast, and almost any "normal, aesthetic" roofs is in the 10s or single digits. So very little solar gain is being reflected away. Once I painted the roof of a small shed white, the people who sit in the shed all day had no way to know I had done that. They commented "it is MUCH cooler in here!" Anyway, all that to say, if you for a white roof, no half measures. A little not white is a lot not white. Ask your coating supplier.
But that significant building mass is definitely a player. The morning sun is blasting your roof with the exact same 300 BTU/hr per sf as the afternoon sun. It only feels different because the building has thermal "inertia" - it cooled off overnight and are only starting to be warmed. If you're the frog in a cook pot, the first couple of minutes probably feel real nice. That's why we get this goofy "duck curve" in electricity generation - the solar panels work exactly when the sun is heating your roof, but the building's mass adds many hours of delay before you feel the need for A/C. I got smoked out of my house about 4 pm today, even though sunlight is from 6 AM to 8 PM. The building's mass carries the heat well past sundown - that's why at 9:30 after dark, your A/C is still working hard. We can't use solar for that, the sun has set. (One answer is to overcrank the A/C when cheap clean power is available.)
In conventional construction like yours, the mass of the building is your worst enemy.
Of course you can add layers of insulation between you and the building's mass, but that's a holding action - the building's mass is still your enemy.
The best efficient designs actually "flip the script" on that, by putting the building's mass inside the insulation envelope. Now instead of storing solar gain, the building's mass is helping resist temperature change. That's a shout-out for Ecnerwal's suggestion of foaming the outside of the roof.
That also puts the foam outside the living space envelope, which I like for a couple of reasons. First, mixing errors can make professionally sprayed foam very toxic, causing odor and illness that just won't stop, ever. People have had to have their entire roofs torn off and replaced to save their homes. Second, all DIY foam and some commercially applied foam is quite flammable... but worse, when exposed to flame, it emits extremely toxic smoke that renders people unable to escape. Outside the living space is better. I would use fiberglass or rockwool on interior rafters, which are non-flammable and non-toxic.
In the west we are very skittish about soffit venting, because it scoops up embers during wildfires, defeating all other fire defense. But if that's not an issue, moving as much air as possible through that attic will help. It will break the conductive "greenhouse effect" happening up there, and make the top of your ceiling no hotter than ambient air outside.
