It seems like originally you thought hosting was the problem but it's really the store manager's time & their lack of understanding of the apparent importance of having a website.
Instead maybe you could automatically generate a website for them by combining data from Yelp, Locu, Yext, Twitter, or whatever other info you can get your hands on. Take the data and find / create a few generic themes that you can insert the data into. Then go to them & tell them you'll host it for $X a month. Maybe over time, you can add support for Yext / Yelp / Twitter / Yelp admin management from one centralized dashboard (given those services allow you to in their ToS / API rules).
By grabbing the data and generating the websites, your chance of selling to them is much higher since they have something they can touch & interact with (not a hypothetical website they have to make themselves). In addition, over time you could build a nearly automated system which discovers restaurants on Yelp that don't have a website, build them one from the info / data available online, and contact / email them saying you can have it live in minutes + will charge $X a month to host it.
2 important things to keep in mind:
1. Restaurants and store owners are incredibly cheap. They're especially cheap since most restaurants have very low margins (1-8%). Many of them use the restaurant to support their family and pay expenses. The $40 a month you want to charge them seems high (from your current website).
2. Don't focus on menus, thats more v2 or v3 stuff. Also, Locu.com is the leader in both getting menu information for most restaurants as well as offering a centralized place for restaurant owners to update their menu. Best part is, even if store owners don't use Locu to manage / update their menu, Locu intelligently crawls restaurant websites to update menu listings automatically. It may be hard to compete with Locu at least initially. Instead maybe focusing on the facts that A. Many restaurants don't have websites but if for $10 a month you can make hefty profits (9 dollars of the 10 profit with enough automation) and B. Store owners apparently don't have enough time to manage their digital footprint / brand. Build super easy tools that let them do so with minimal time spent + also collect / publish data on the benefits of having a digital brand when you're talking to restaurant owners.