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EDIT: actually in full screen mode (and tablet mode for the future), these kind of things might help.
I agree.
"Would this be the right click menu?"
There will be no need for context menu, toolbar icons will be what is in context, remaining toolbar items will be hidden. Toolbar is activated with context tool icons, trigger by what the user does ( trigger by selection e.g.)
I hope I am clear, pardon me it is just a small idea to have more focus on the canvas and tools are in the background, and called in the UI when needed.
Makes sense?