Many have had their secured card upgraded to unsecured. Try talking to a banker in the branch, or try to get a hold of an underwriter directly or call EO.
You do not need a checking account to open a credit card account. Since you are already a Wells Fargo customer you should be able to apply online on your own as well, or you can do so at the branch. I recommend doing it in the branch since the personal bankers can help you put in a good word with the underwriters sometimes if you have good banking relationship.
Also, Wells Fargo seems to be very stringent when it comes to unsecuring cards. They are an extremely conservative lender.From what I have seen, the individuals who had their cards unsecured, would have been approved for other prime cards as well.
JPMorgan Palladium (100k), AmEx Platinum (NPSL), AmEx SPG (46k), AmEx BCP (42k), Chase Sapphire Preferred (47k), Citi Prestige (31k), Citi Thank You Preferred (27k), Citi Executive AAdvantage (25k), JPMorgan Ritz-Carlton (21k), Merrill+ (15k), US Bank Cash+ (22.5k), Wells Fargo (12k), Bloomingdale’s (12.4k), Chase Freedom (5k), Discover IT (5k).