An update to my own question in case it is of use to anyone else contemplating a similar move. I went ahead with changing countries (US to India) and, a month or so down the line, am happy to note that everything went extremely smoothly. I am able to access and install all the apps that I had purchased on the US store and they get updated without any issues as well. Here is what I did:
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I backed up all my iTunes purchases; apps, music, movies and books. Since iTunes 12 doesn’t allow you to back up apps I did so on a spare Mac on which I installed iTunes 11 (there is still a supported version that is available from Apple.)
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I called Apple Support as @RosemaryOrchard had said that they had helped her transfer purchases over. They weren’t able to do so for me but told me that I should have access to all my purchases as long as they were available on the Indian iTunes Store.
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I downgraded my iCloud storage plan to the free 5 GB tier (I was on the monthly plan and had to call Apple Support to have the plan end earlier than it originally would have) and cancelled my only subscription, which was an annual subscription to Overcast Premium. Interestingly, I continue to have access to Overcast Premium and expect to have it until my annual plan ends in April 2019.
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I had a fair bit of store credit, which I used up with the kind help of the folks here.
That was it really and luckily everything works just fine. I found this article by Jordan Merrick to be extremely helpful.