>I got the job through a summer internship, which allowed me to bypass the rigorous 8-interviews-in-a-day hiring process. And I lucked out... completely escaped having to code over the phone.
I'm not trying to troll. However, I honestly do consider you landing a Google engineering internship/job with those school background (and zero coding experience outside of school up to that point) being pretty lucky. Consider this guy[1]. I believe he would've most likely gotten the internship had he gone through the same interview process as you. I know that's just my subjective opinion. However, the bottom line is he went through a very different (arguably harder) interview process than you did. It's harder in the sense you could have very well failed had you been asked to code over google doc + phone. The key factor here is this process that Google uses everyday to turn down countless competent but not extraordinary people - you did not have to go through it. That is the basis I deem you lucky.
There is a certain level of respect (among other befits) given to former or current Google engineers among hackers. And I would argue that is the case largely because of the very difficult process that they had to through to become one. I can totally understand why you had the sense of inferiority and insecurity of your coding abilities, having not gone through that process.
Of course none of this makes your point of everyone is good at different things and you should not beat yourself up any less significant. I agree with you on most other points. I'm also happy for you that you've overcome these self defeating thoughts and have proven to yourself. As some one else mentioned in the comments, the problem was you being you own toughest critic.