As a manager, I would listen to the IC's request, say "I'll see what options are available, let's come back to this next week in out 1-to-1", and then go to my boss to see how much time we can offer/how to implement a vesting holiday.
If the options are: lose someone for 6 months, or lose someone completely; I'd push strongly for the former.
You're a better manager than any of the ones I had at Google. That said, your boss might laugh _you_ out of the room, bringing us back to square one. He/she doesn't cherish the idea of hiring a replacement for the duration, or scaling back what he/she promised to _his/her_ boss (whew, those gender pronouns make it a mouthful). It's one thing if you need to care for a sick relative or something, any tech company will make accommodations. But to "travel" so you could gestate your startup idea -- that's pretty much a GTFO right off the bat.
It's been a few years since I left, I don't remember. I do remember there are level and performance requirements, too, and there's no guarantee that they hold your old spot for you when you come back. So you do very much depend on the benevolence of your corporate masters.