Unfortunately, all the GFSI programs will require documentation, and in the majority they all require the same things such as overarching quality requirements, procedures, all documentation relating to record keeping for your manufacturing process. It's something that you can't get away from, it's about records and having proof/evidence of you doing what you say.
You say "we are constantly creating documents" you have to ask why, are they necessary, being created just for the sake of creating, to fix a non-conformance, to record stuff you may not need to record?
Just go to the SQF site, you'll fall under the following:
FSC 22 - Processing of Grains and Flours: SQFI | SQFI Code Selector
Part A: Implementing and Maintaining the SQF Food Safety Code
Module 2: System Elements
Module 11: Good Manufacturing Practices for Processing of Food Products
As you have FSSC, you'll should have the bones and muscle in place, if not more, of the requirements for SQF. You'll just need to review and do a gap analysis to see what's missing. But you won't be able to completely get away from not having records and procedures etc, but you can be smarter about it.