Which glue should be used for adhering thin paper?
To be honest it sounds like you might be being a bit heavy handed with all of the adhesives you mention it is often the case with adhesives that less is more. 

White glue : you will get the most control if you apply it with a brush, if you just squirt it onto the paper and then spread it around it will soak though. You could try getting some cheap nylon brushes (the flat type are best) and use the glue from a small pot rather then direct from the tube and keep a piece of scrap card to make a few strokes with the brush onto to make sure that the glue is evenly distributed on the brush and take off any excess. You only need a really thin film to get a good joint, ideally it should be thin enough to look  transparent rather than white. 

Spray Mount : again you only need a very light mist for it to work, try spraying from further away and just use one quick pass over the paper. 

Another option is double sided tape, this tends to be a very neat and clean solution although there is a bit more effort involved in cutting it to the right shape. Usually the best approach for complex shapes is to apply it to what you want to stick before you cut it out so you cut the cutout and the tape at the same time (obviously leave the backing on the reverse side while you do this.