I would let the current lender know that you are satisfied with their service and are heavily considering their proposal, but are concerned about fees and that you'd like some time to compare with others. Perhaps the current lender will become more competitive. If the current lender feels another credit inquiry will reduce your score, they can provide you with a copy of the credit report they have (this may be required). You can bring this report to another lender so they can put together a Good Faith Estimate for you.
I'm not a lender so I'm not sure this is the case, but from your description it seems that your first mortgage may be larger than the current limit of $417K to avoid a Jumbo mortgage. Ask your current lender if this is the case. If so, you may have less fees and an even better rate if you keep the first below $417K.
Best of Luck
I'd be careful here. The general answer to your question is to find a different lender who you can then price compete against your first. However there is always a possibility that you can or will affect your credit scores by having multiple lenders officially inquiring about your credit history. If you are at or near a credit pricing threshold, 680, 700, 720, etcetera, then even a small change in your middle credit score might affect the pricing of your loan and the interest rate that you receive.
If you are doing this in the Chicago area (and I can't tell based on your zip code designation) I'd suggest contacting Dan Larkin with Professional Mortgage Partners. He has been in the business for a number of years, and he is by far the most consistently great lender that I've worked with over 5+ years of being a real estate agent and 2 years as a residential closer for a title company. Dan can be reached at 312-952-8068 (cell) or 847-277-1781 (office).
Dan and I have no formal arrangements that benefit me when I refer him to clients other than he does not upset my clients nor mess up their deals (as almost every other lender that I have worked with has done at one time or another). Good luck.
Broker Associate, Sudler Sotheby's International Realty