Want to raise my ceiling and have insulation questions

Hi. I have a small ranch house (560 sq ft). The ceilings are at 7 feet with a very small attic. The middle of the attic is between 3 and 4 feet high at the most. Right now there are only 2 gable vents and a strong attic fan - 1900 cfm I believe. There are no soffit or ridge vents.

I originally wanted to completely vault the ceilings but I do not think that is possible with no soffit vents or ridge vent. And I do not want to sprayfoam and have a hot roof system.

Instead of completely vaulting the ceiling, I am thinking of just raising the ceiling rafters to the upper limit for an effective rafter tie and making a new flat ceiling on top of that. My concern is insulating. A good portion of the roof rafters will now be in the conditioned portion of the house and contain insulation and be drywalled up the new ceiling.

Here is what i want to do: I want to leave a part of the attic intact on the side with the attic fan. I would install baffles in the rafters and use batts up to the new ceiling. I would then insulate above the new ceiling with batts. This would leave a small gap between any ceiling insulation and the roof. A portion of the gable vent opposite the attic fan would also still be there.

With having a gap present for all areas of the roof and keeping the ability to run the attic fan, is this a viable option for properly insulating and causing no harm to my roof?

Thank you for any help and suggestion!!