How to write a survey paper?
The point of a survey paper of the type you are discussion (as distinct from a systematic review), is to provide an organized view of the current state of the field.  As such, you should not be attempting to cite every paper, but only the ones that are significant (which will still be an awful lot).

Writing a good survey paper is hard, and there really aren't any good shortcuts: you do need to become familiar with the content of a very large number of papers, in order to make sure that the view you are presenting is sane.

My suggestion, based on my own experience in this area, is to use the following iterative process:


Begin by collecting a large pile of papers to survey.
Based on your experience and a few initial readings, hypothesize an organization schema for the field. 
Start reading (mostly skimming) and organizing your collection of papers you read using this schema, including noting which ones are most important and which do not fit the schema well.
As you find significant numbers of papers that do not fit the schema well, adjust the schema to better fit what you are actually finding and shift the organization of your collection to match.
Add new papers to the "to be read" collection based on the adjusted schema, then return to reading and organizing.


When the process converges to a stable schema and an empty to-be-read pile, you will have a well-developed view of the current state of the field and be in a good position to write a survey.  Note, however, that this may take a number of months...