You as a consumer do not have access to wholesale mortgage lenders.
You need to understand that lending market is hyper competitive. Not every buyer is a good fit with every lender. There's no particular advantage using a bank over a mortgage broker in fact I would tell you that most buyers are better off with a mortgage broker who isn't married to a single bank but has dozens to work with based on your profile. You're over analyzing. Today's rates are half of what the 50 year average is and 1/8 or a point means next to nothing in the long term. What matters is the ability of the lender to efficiently process your loan with the least amount of aggravation on your part and give you a final loan commitment in a timely manner.
That said there is a huge difference in the service you're likely to get between various lenders and more importantly there's a big difference between what the banks like Wells Fargo, Suntrust and BOA can do in terms actually performing the task you hire them for (Giving you a competitive mortgage in a timely manner) and what a good mortgage broker or smaller bank can do. As someone who closes an average of one transaction a week, I can tell you that I will never allow a client to use BOA (their that bad), and while I personally like a number of originators at Wells and Suntrust they haven't been able to close a single transaction on time in the past couple of years and my buyers all report that both banks were nothing agony to work with.
My advice is to ask your buyer broker for some recommendations, using one of their preferred lender will enable them to jump in and help push things through if necessary.
If you aren't working with someone, feel free to contact me directly through my profile here on Trulia and I'd be happy to give you a few names and numbers of some excellent local lenders.