Find the phase angle between two functions
Additionally, it seems to me which function leads which is rather relative as I can shift any function 360 deg, any easy reconciliation?

Absolutely. What is leading or lagging is up for interpretation/definition. Personally, the only definition that would make sense to me would be that any lag by more than 180° is actually a lead. Maybe that book defines it otherwise, or it's plain inconsistent/underdefined there.
Re: your angle: Well, no matter what happens, the result needs to have a &quot;last digit&quot; of 5°, so we can directly conclude that the book's solution must be incorrect.
Let me try your calculation: \$-\sin(x)=\cos(x+90°)\implies i_1=-\sin(337t+50°)=\cos(377t +140°)\$, and \$140 - (-65) = 205\$, so I'd agree with you.
By the way, you say you've been fighting a lot of mistakes in this book. Note them down as errata (even in rough form, just scans/readable photos of paper or similar), and post them in your year's forum (or however you and your coursemates communicate). 
You will a) earn eternal gratitude of peers through little extra work, b) if you did actually do something wrong but the book got it right, you get free corrections, and c) at the end of the whole circus, you drop an email to your prof and tell her or him that hey, you went through a bit of effort, whether they might be willing to share these errata which the course looked through with next semester's students. That might lead to you being asked to type them out for money, or to the professor more intensely reviewing course material.