Semi-crazy maybe. Tne porch would most likely leak. Stone layed on a wood deck would likely rot & leak/fail eventually. The stone with the log cabin could look nice though.
If you did the extra basement space, I would want a concrete deck to lay the stone on as well as waterproofing membrane. My experience with underground rooms beyond the main building is they usually leak or are at least are damp.
Could you just pour a slab on grade with the proper foundation and then cover with stone?

There is a company call stone deck that has a system for putting stone on top of an exsisting deck. I looked into that a while ago, but I decided to go with the Schluter system. (My deck is about 75% complete.) They make an membrane to go under stone or tile that makes it completely waterproof, and will take freeze/thaw cycles. It has drawbacks and advantages. It's expensive, but then there's no staining and refinishing. I had trouble getting approvals from my building department. It took time, but the approvals came through. I went with an outdoor rated porcliean tile but, I saw a deck in my area that used slate. It look great.

You have to find someone who can lay tile well and can follow instruction. Your not likely to find a deck builder who has had experience doing this in your area. I wasted a lot of time chasing the only one in my area who had done this before. They were not that close and didn't want to come out here.

I found an experienced deck builder in my area that was willing and to try something new. His men, and some subs, are installing the tile, the point is that the deck builder is standing behind the whole thing. I was ready to go with a comtractor who wanted me to get someone else to do the tile. I felt uncomfortable with that. Who's responble if somethng goes wrong?