Update from my most recent trips to India. It appears that now you can select different payment methods or set a different default contactless payment method by opening the (US region) Wallet app directly (at least on Android) when in India. However, curiously, it is still impossible to do either of those things from the wallet "tile" you get when you swipe down from the top - that still shows up greyed out as soon as you land in India, and only allows the default contactless payment method to be used. I did not try to add a new payment method while in India, so I'm not sure that's possible yet.

But I wouldn't recommend relying on this, never know when Google might change things again based on their whims and interpretation of Indian regulations. Best to set a reasonable default in the app before you land in India, and always have a backup physical card or two to use too. In any case for higher payment amounts you'll need to have a physical card on hand (e.g., hotel bills) as usually contactless is rejected above some threshold.