what are some good exercises for driving theory into my brain and memorizing the names of the notes on the fretboard?
Using it.

Theory isn't really about exercises, it's not exactly something you can drill - it's simply about understanding what you're doing.
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That's nonsense! There are thousands of exercises that can be done for theory. Get a transcription of a piece you enjoy and analyse the notes in, see what chords are put where and to what effect, what scales/lciks are used over chords etc. For just basic theory drills there's always http://www.musictheory.net/
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