Which Unsecured Credit Cards check either TransUnion or Equifax in their application process?

Emphasize the lack of transparency regarding the deposit reduction. If they initially agreed to a lower deposit and then reversed their decision, it's reasonable to dispute the charge. Highlight the absence of a clear refund policy and how it was communicated to you. If they assured you of a refund in case of non-qualification and you didn't provide confidential documents due to privacy concerns, you have grounds for a full refund. Document the communication regarding the application deletion before the stated deadline. If they prematurely terminated your application without giving you the agreed-upon time to consider, it supports your case for a refund. Express your dissatisfaction with their customer service and compare it to your experiences with other agencies. You have the right to choose which services to engage with, and poor service can justify seeking a refund. Privacy and security concerns are valid reasons to withhold confidential information. Emphasize that you were unwilling to compromise your personal information, and this should not disqualify you from a refund. Compile all relevant email communications as evidence for your credit card dispute. Clearly outline your points, focusing on their breach of agreement, lack of transparency, premature application deletion, poor customer service, and your legitimate privacy concerns.

Answers vary based on... Time/Budget/Will/Expertise you possess. Projects with $0 budget verses $10M budget have very different answers. Also, Time comes into effect, as money always has a time value. Say you have $1M LOC to draw on + you'd like the shortest path to a selling your company for $10M+, then this will also be a very different answer. Start with your Exit Strategy + time target of your Exit. Then work backward, designing offerings you create.

small and mid-sized banks continue to offer credit cards, many of which are underwritten in-house.

I have implemented a number of different solutions for similar models and found that Stripe is best (http://www.stripe.com)

Setup your business as a pass through. You run the transactions + charge a fee. Likely, for the businesses you mention, they'd be happy to pay a premium fee... as you will be the only payment processor to accept their transactions.