As always, a terrific trip report!
IMHO, For Jaipur, I would have chosen the Oberoi Rajvilas over Rambagh Palace (I have been to both). Curious to hear your impressions of the Rambagh palace.
When you are at the Oberoi Mumbai, I wonder if you can post pictures of the Capital O Lounge, which is a recent offering for those residents in suites.
Cheers and safe travels!