If you are sure about consulting then here's the scenario
- You can focus on English speaking markets in the EU with London being the major hub and Amsterdam being the next best option. I have seen a few of my Indian classmates get into offices in Brussels and others
- While you're right about securing a visa being difficult for Indians wanting to work in consulting in Singapore, it is not impossible and you can definitely target companies there
If you have an active H1B or any other authorised work permit in the US, you will have a lot of chances to recruit in the US. Without an active work permit US is just not an option
Outside consulting, big tech has no issues in sponsoring visas either in Singapore or US. Amazon recruits heavily for their Luxembourg and London offices but I suspect you can make that change now and don't need to go through INSEAD for that.
For middle east and Australia offices, I second Pabpinors comment - Australia and other offices in SEA are a good bet
You have a great profile, if you target the specific offices you want to get into, network effectively with INSEAD alumni in those offices and prepare well for your interviews, you should be fine. That said, with Covid, things will definitely be tougher and more uncertain over the next year or so