TLDR: At the bottom of my reply, I offer a fairly easy-to-implement solution.
That's really awesome of you, both to take the time to reply, and to look into the matter. I truly do know the relative difficulty/complexity in what I'm asking (again; I was an iOS developer) but I assure you: this would be the last bit required for me to discard pretty much the rest of my tools, personally, and I think you'll be surprised how much a difference it makes.
Regarding the control center workaround, yes, I do know you can lock the device orientation. The problems this introduces are twofold:
1. Naturally, the interface doesn't rotate with the device (as it has been instructed not to do). The hassle here is that it inverts all of one's direction-sensitive commands (easily ignorable), but worse, it does things like move the undo button to a new location with every 90-degree shift of the device. This is harder than it sounds to mitigate, mentally.
2. The iPad is a capacitive device. Without going too deep into the mechanics, suffice it to say that when you touch the screen, you're actually touching a point millimeters ABOVE the point your brain "thinks" it's going to contact. We did a bunch of OS-level jiggery-pokery to "trick" the users' brains into believing that the point they're aiming at is actually what they come in contact with (it's functionally an offset upwards that depends on a slew of things, from orientation, to angle of use, to stylus vs finger, to whether or not the keyboard is on screen. In short, we cheat.
Thing is, that offset rotates with the perceptual screen orientation (that is to say, the amount and direction we "cheat" is device-orientation-specific). This means accuracy drops by more than an order of magnitude when you flip the device with the lock on (to see this for yourself: open Art Studio. In light gray draw a simple X or +, thin line. set your lock, then turn your iPad upside-down. Using the best stylus you have (indeed, this is the best test OF a stylus, without the 'flip it upside-down' bit), simply try to place a dot where those two lines intersect).
So the UI already rotates with the device orientation. I'm assuming you're simply tapping the OS's native ability to do so. Fair enough. let it continue to behave that way. but if you investigate the UIDeviceOrientation (specifically the beginGeneratingDeviceOrientationNotifications event) you can watch for the shift from UIDeviceOrientation=1 to UIDeviceOrientation>1 (Apple, in their infinite wisdom, decided that, starting vertical and going clockwise, the respective values are 1, 4, 2, 3. I have no idea why). The trick I'd pull, though, if it were me, is that I'd simply programmatically rotate the canvas 90 degree in the SAME direction when the event fires. The UI will realign on its own, and the canvas will appear to have simply stayed put, orientation-wise. You may need to compensate laterally for the change in the X/Y coordinates of the canvas's origin relative to the viewport, but it means you can forgo having to recalculate all the BS with gradients, transforms, flips, resizes, etc. and simply apply code you've already built (rotate/pinch) to keep the canvas in a natural-feeling position.
Offer stands, man. You get this done for me, you send me a paypal link. In. A. Heartbeat.
EDIT: Thinking about it, one could even keep the canvas entirely bound to rotation, degree by degree using the same trick, but I'd be happy even with the cardinals