I'm an application developer full-time but I'm trying to make a shift from working for someone else to starting a company primarily focused on custom application design/redesign. However, my target clientele operate during the same hours I'm at work in my normal job. Any advice would be appreciated for how to best build a new organization & sales while still working for another company.
First, commit to yourself that you will never cheat your current employer out of hours you owe them. If you're salaried, you the expectation is that you do the work they have hired you to do, whether it takes 40 hours or 80 hours per week to get it done. The rest of this answer assumes you have some flexibility in your work hours.
Then, regardless of whether there is contractual language in your employment agreement about side-work, clear this activity with your current employer (in writing, if possible). At best it is a courtesy to them. At worst, it's a safety for you in case they decide you owe them a piece of your success (For example, making use of any specialized knowledge they provided to you). A very sticky point (according to some lawyers I know) is when you take time off during hours you would normally be working at your day job to work on your side job (such as sick time, vacation time, extra long lunch with hours made up later, etc.). A pernicious company with a good lawyer can use that against you. Getting agreement from your company ahead of time avoids much of this type of headache.
Next, assuming you can take time off during the workday (Vacation/PTO, make up hours later, but never use sick time), schedule some time during business hours to do the work that cannot be done at any other time, such as meeting with clients. If possible, schedule these times either at the beginning or at the end of the day (it just works better to compartmentalize your time in your own mind).
FYI, I have found that corresponding via email is actually very productive, and nearly eliminates the need to meet face to face during business hours. This usually happens when trying very hard to come up with a mutually agreeable meeting time. Finally, one of you simply says, "Let me just email this to you, and you can get to it when you have a chance." Problem solved. (Admittedly, face-to-face meetings are able to make decisions faster, so if you go the email route, you'll have to become a master at following up.)
Finally, any work that does not require direct interaction with a client during business hours can be done in your off hours. You're basically working two jobs at this point, and you'll be running yourself ragged. It can be exciting, though, if your side business begins to be successful.
Never, ever, use your employer's resources for your side job. This includes computer, internet access, software licenses, contacts, etc.
You need to understand that if your performance at your day job suffers in any way due to your side job, your employer has a right to ask you to stop it. If this happens, you'll have to decide whether your side job can support you full-time.
To answer the question: I see no solution other than either hiring/partnering wit h someone available during the day, or delivering a product that needs no realtime marketing or support, or quitting your current job, or selling your product idea to your current employer, or shelving the idea until you are at a better point in your life to pursue it.