I went to India with my husband in Feb 2010, and he has severe gluten issues (but not casein or dairy).
If you don't have dairy sensitivities then yogurt, lassi, paneer (often cooked in heavy cream) is fine.
Goat and lamb curries are delicious. Most chicken is now factory-farmed so do more goat, lamb, and fish.
They do have pastured brown eggs, when I was in Kolkata they called them Desi eggs and even the maid knew what they were!
You will get vegetable oils because they are cheap just about anywhere unless you have a cook at home and go to the grocery store yourself.
Stay away from all fried foods and naan, puris, breads, wheat of all sorts.
Bhajra roti is made from millet. Rice is fairly benign.
I would try to have animal protein and fat at each meal and have vegetables and potatoes too. Minimize beans/legumes/dals.
Eat ghee but stay away from dhaldha (fake hydrogenated ghee) - butter is more reliable. Most dairy has become factory-farmed unless you know the cow in the villages.
Don't overdo the carbs - Indian people are obsessed with sweets. If you can handle dairy then rosagolla, rasmlai, sandesh, kheer or payesh (rice pudding) are made from milk as a cheat. Better than the wheat sweets like gulup jamun.
Ask if any flour is used in foods you eat.
Hiring a cook is pretty inexpensive the US equivalent of maybe $5-15/day.
Don't eat raw things unless like a coconut, banana, that have a peel. Too many parasites.
Avoid street food which is mostly wheat deep fried in vegetable oil. Most illnesses come from this too.
Avoid ice, juices, and smoothies unless from a 5-star restaurant - my Mom got salmonella at an Indian wedding!
Sweet and Salty Lemonade with Mint is not bad - again from a high end place.