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.
If the options are: lose someone for 6 months, or lose someone completely; I'd push strongly for the former.