If you do end up going to another lender, provide that lender with ALL of the updated documentation that you provided the first lender. That should prevent any additional requests for paperwork.
This nonsense of needing an underwriter for a preapproval is likely becasue you dont have a knowledgable loan officer. Im not one, but there are a ton of good ones out there that can give you a basic rundown of how much home you can afford and what loan program you will likely fit into.
When you find your dream home...thats when you bust out all of the documentation and cross yout t's.
The answers below are great and spell it out very well. I work in Stockton and if you have the packet of information you've submitted and would like to have me review and submit for your pre-Approval I would be happy to. I communicate well and often and that is important. I also represent the home buyer when looking for a home. Our office has 18 years of local, Stockton mortgage lending and real estate experience. If we can help our number is 209-952-4574 and ask for Eric or George.