You cannot.
To think that you can completely bypass the crowds in the worlds second most populous country in the world, would be mere wishful thinking.
Based on your itinerary and plans, you could travel and live in pockets of quite, tranquil and nature in this country, but to reach those places you will have to wade through some tight spaces first.
Almost everyone comes to India to be blown away with the stark contrast of things, so while you will enjoy plenty of tranquil, there will also be periodic bombarding of your senses.
This is part of what India is and has to offer.
You could visit some cities during off season, and have the place a bit to yourself, but to what end? The noon sun beating down on you, washing everything in unbearable white, or the incessant rains making it impossible for you to step out and explore.
To put things in perspective, Hampi is crowded post monsoon, for good reason – this is when the river Cauvery is in it’s majestic full flow, rice fields are lush and vibrant and the early hours of dawn/dusk cast a beautiful golden glow on its UNESCO recognized world heritage ruins. Traveling at any other time could mean, that you would miss seeing Hampi at its glowing best.
You traveled across the globe to see this vibrant country, so see it in its natural, beautiful, chaotic, jam-packed entirety.