Which glue works best for paper sculptures I have tried several types of glue but, have yet to find the perfect glue for my needs. For instance, I'm creating a miniature tree and need to glue multiple small leaves onto a branch. 

I don't want runny or slow drying glue that the leaves slip off before the glue dries or nearly dries. I often get a few leaves on to have them all fall off as I try placing another leaf. I then wind up having to glue them all back on all over again. I don't want to have to just glue a couple on then wait anywhere from 5 to 10 minutes or more before I can glue anymore on. Sometimes I have to sit and hold on one leaf at a time until it dries enough so that it doesn't slip out of place or come off all together. 

I need the glue to dry clear and matte. It will also have to work with card stock, bond paper, brown paper(such as used to wrap packages for mailing). Sometimes painted with acrylics or water color paint. Also I run into the problem of the piece I'm trying to glue sticking to my fingers or instruments as I lift of the piece. 

Hot glue doesn't work because I have lots of small pieces in one area and it will accumulate to much glue not to mention other issues with it. The glue I want works like this: I put glue on a piece stick it where it goes on 3D objects and it stays put while gluing other pieces next to or on top of that piece. It seems like it would be real simple but, what it seems to be and what it is are 2 different things.
Given your criteria the glue I would think should be tried to see if it fits your needs is cyanoacrylate glue, or CA glue. This can be commonly refereed by brand names like Super glue or Krazy glue as well. They are advertised and being very versatile when it comes to applicable mediums and have very fast drying times. 

Looking at one brands technical specifications as a base line we can see that it


  Dries in 10-45 seconds, no clamping required.


Most CA glues dry at or near those times as well. Careful working with the stuff as you a likely to get some on your skin and it bonds skin very easily (Recently used it to repair my glasses).  

Now what you could so with this is use it as a placement glue. Using a little just to get the leaf in place so that you can continue with a longer setting glue without concern of the leaf moving. 

Would clamping options apply here?

I don't know how your leaves are made nor how they touch the tree but have you tried clamping options instead of looking for a fast setting glue? Some simple like paper clips( which you can mold to conform to shape if need be) or even something like binder clips? Perhaps if you have something small and light weight to help hold the leaf in place your choice of adhesive might no longer be a concern.