Here is an idea:

Focus your marketing on one type of business that you have had success with in the past. Example: veterinarians. You can still do work for other clients that approach you but, for now, focus on this target market.

The advantages are that:

1. You stand out from general website designers.
2. You can show them relevant examples, know their terminology, and specific needs.
3. While your existing customers might not want to introduce you to competitors, they would have no issues referring you to complementary businesses.

For example, if your target market is real estate agents. Ask your real estate agent to introduce you to bankers, home inspectors, real estate lawyers, etc. Then take them out for coffee on a regular basis, build relationships with them, and tell them that you design websites for real estate agents, and they can refer you to agents they work for, and you can refer them to agents you work with.