Websites need design, visual assets, integrations, customised features, etc. It’s definitely a volume trade: you need to primarily be concerned with new biz, but it’ll be viable for a long time to come if you know what you’re doing .
I think it heavily depends on your network and the market in your location. Sure, if you're in the Bay Area, freelance might not make sense; but find a city with 100-200k population and start building a network among small-business owners/operators and you can do just fine.
If 2-3 represents all of them then I would just put in conversation with them that you'd appreciate any referrals they can make and if you think it would help offer them some financial benefit for it (the amount is culture dependent, I find).
If you exhaust them and the rest of your professional network, try local industry meetups (especially industries that you have made sites for before).
If all else fails then try your luck in the forums and job boards. I suggest taking on small stuff to get your foot in the door and aggressively vetting the personal and business characteristics of new clients for this way.
I'm back to full time employment though so make of that what you will!
I'm also at full time employment but I miss the autonomy and working from home.
For startups it’s even more important.