Hi,
I was just from West Papua. Travelling just for fishing and visiting tribe.
For a very remote tribe as you asked, it will cost a lot, especially for transportation, food, and drinking water.
A bottle of drinking water in bali oly cost some 40 cents USD, in west papua/wamen it will cost you us$1,5 per bottle of 500ml.
I visited Korowai, people who was still living up in the tree. i fly from Bali, then an hour drive and 10 hours boat ride of 184 kilometers cruising upriver. The same distance if i would visit Asmat tribe, then we walked 4,5 hours to reach their closest settlement thru jungle, and stay with them for few days.
The food, sanitation, malaria, snake could be your nearest treat. We hunt, and we had fish, jungle rats to eat along with the food we bring.
I was visiting 2 tribes last month, the Dani people and one in Sumatra, Mentawaian. This month perhaps i will see Yali people in Papua. Since i was visited those 2 places before, i know now the best and cheapest way to get there.
If both of you would to go, better split the cost. and a group of 4 is better, because fit one car, fit one boat, and fit 2 rooms in a motel, the maximum efficiency travel.
I will go to sumatra for mentawaian in couple weeks, there we have to go upriver for 54 kilometers, slower boat and takes some 5-7 hours, then walk and hour or two and we arrive at their house/what they called as UMA. Mentawai is so beautiful, with clean river and jungle. The river are seems to be safe to drink direct but i would prefer to boil it first. perhaps you guys can join me.