Insulation requirements are specified by IBC. You're in climate zone 4. Table N1102.1 specifies the requirements. It's either R30 continuous or R38 non-continuous. They consider it to be continuous if the full, uncompressed thickness of the insulation extends over the top plate at the eaves. If that isn't possible (usually isn't due to available space), then you must install R38 everywhere else. For reasons I'll discuss below, you might want to stick with R30. It might not be code, but it's also not as thick.
Cyd and I talked about your insulation location, and decided a couple of different things. For starters, your house isn't designed to have insulation installed against the roof sheathing. That should be avoided to prevent moisture build-up that could prematurely deteriorate the roof sheathing and shingles. If your roof has soffit vents and a ridge vent, you should be sure to have enough clear air space against the sheathing to allow for free air flow. There are actually calculations you can do to determine what this clearance should be, but I would shoot for at least 4" overall. If you have less at the eaves, that's fine. They actually make foam spacers for this purpose that slide down against the roof sheathing and leave a clear path for air to travel from the ridge vent. Given how little space in the rafters that you have to work with, the proper way to do it would be to frame out ceiling joists below the rafters or pad down to make the joist cavity thicker. You may not want to do this for head height reasons, but it is the "right" way. Padding down also contributes to thermal bridging, whereas a separate ceiling joist can have insulation installed on top of it.
I would also consider beefing up the wall insulation to R19. R15 is the code requirement for a wall that is exposed to the exterior, but what you really have is a wall that's exposed to an attic space that will be super heated (110-115F is easy on a pleasant day), making the temperature differential across the wall much higher.
It looks like the space has its own mechanical unit, so I wouldn't worry about the insulation between the attic and the rooms below. It won't hurt anything, and may reduce noise transmission.
You can also build up the insulation from one or more smaller units. Get an R15 batt that fits in a 3-1/2" stud cavity, then install R19 batts on top of the studs in the opposite direction, etc.
There are also an assortment of spray applied products. Open-cell and closed-cell polyurethane foams, sprayed cellulose, etc. We don't think any of them are appropriate here, given the risk of moisture build-up on the roof sheathing mentioned above.