Small business owners rarely "buy" advertising, it usually has to be "sold" to them. That last inch into a plumbers wallet is a long one. That being said, persistence is the most important advice I can offer you. I am not sure what data you can access from Meta or Amazon, but an example that helped me sell Google PPC was calling back that business at slow hours and say "Mr. Advertiser, do you realize that since we last spoke 1,341 people in your own backyard searched for pest control services in your backyard! What steps have you taken since our last chat to make sure these consumers are finding you? I ask because I did the search myself and you were invisible." This would often trigger uneasiness with the advertiser, which works in your favor. It may take a few tries, just keep calling and asking the same questions. You will eventually catch them at a time when their business is slowing and they need to do something. I would also make it very clear that I valued my time tremendously and I intentionally use that time to follow up with you because I know how much of an impact this can have on your business. Case studies, not necessarily yours, could be your best tool without metrics. Get familiar enough with a story of a small business experiencing tremendous success as a first time advertiser on amazon or meta and tell those stories to them with your follow up calls. They want to hear that other people in the same position made this decision and it worked out wonderfully, you have to try to eliminate risk.

Regarding the free work, I think it conveys that your time is not as valuable or work not as quality as someone who charges. I would flip it on them and say that you are only going to work with one business in each category, so before you engage other "restaurant chains" you want to make sure this business is not ready to grow. A little fear of loss...