Building upon what Rawkstarscotty said, you could do the same while only letting yourself use the wood that comes from the optional chest spawned upon world generation. Though that may be a little too hard.
You could also try to play in only a small, resource rich chunk of custom terrain in the middle of a void. A little like skyblock but a much bigger chunk of land and no cobble farming and all that, just so that it stays survivaly and not to grindy.
Edit: Was in a hurry while writing this, I shall continue in more detail. The idea was, as said above, to have a floating island or landmass. At first, it would be like normal survival. However, as soon as you begin to run out of things to do, you will also have run out of resources. If you are playing with other people, then this would probably end up sparking a small resource war or at least a panic for people to get all ores they can get their hands on before others get them. This would take away from the exploration a little, but if there were multiple islands/landmasses made up of different biomes, ores, etc each it would still be interesting. Especially if they were very far apart, as you would have to look for them then.
Another idea for a handicap similar to Rawkstarscotty's would be that you are only allowed one of each tool. This would make anvils a must-have, and make the unbreaking enchantments very useful.
Yet another edit: .-. If you wanted to, I could try make a make like the one described above in worldpainter for you.
