You already have all the info you need to make a decision..
Your trip is in 4 months (12 weeks)
Your friend is 6’6” and all of 350 lbs.
Your friend is almost 140 pounds overweight!!!!
There is ABSOLUTELY NO WAY he will be in good enough shape for your trip. You can not lose that much weight in that amount of time in any kind of a healthy way. An aggressive healthy weight loss routine would have someone losing about a pound of fat per week. You've got 12 weeks. Even if he started right now, and doubled that healthy weight loss rate, he still would be nowhere close to where he would have to be.
At this point, you just need to break it to him. He hasn't put in the work necessary and consequently, he can't come. I can tell you that if he hasn't been motivated to get in shape, buy gear, etc, he was never all that serious about it anyway.
Now how to break this to him, that I can't help you with. But if he's avoiding you on the topic (ghosting you) then it sounds like he's already made the call for you. At this point, all you have to do is say - "hey man, you were blowing us off so all we could do is assume you weren't coming. We had to make plans that didn't include you."