In an effort to help and indeed from personal experience over the last 20 odd years as a website designer, the scatter gun approach works - its kind of luck of the draw.

Clients come from a variety of avenues, some from networking events, some from searching using the appropriate words applicable to service and some just appear. Sometimes mailshots work, sometimes they dont and sometimes email works and sometimes it doesnt. Also cold calling works periodically when the moon aligns.

I guess what I am getting at is dont close any avenue, do networking events and carry business cards wherever you go. Learn about SEO and do it - if you cant in todays market you will not survive.
There is plenty of room for good website designers, hence my candid response.
Might I suggest you break your days down to doing all of the above, targeting different market sectors each day as today they need it tomorrow they have it. The day after they might need it revamped and above all dont give up.