I’ve been thinking about this a lot actually. I think one possibility is to build networks of people to help grow and distribute this food communally. In my area there are a lot of fruit trees but much of it goes unharvested, is wasted, and can even be a nuisance since it attracts rats. This is a problem to the extent that most public land managers won’t allow fruit trees to be planted. So the solution is to get some friends together and pick the fruit. Then it can be distributed to the community. I heard there is someone in my city doing this already but in a different neighborhood—I may reach out to them to see how they got the ball rolling.

I think that would be an easy way to start but the idea could be expanded to include foraged foods and gardens that people don’t have time to maintain. I think it’s important for people to first see the benefits of what you’re doing before going too far outside of what is considered normal. Once you have that reputation as helpers, you can push for more radical ideas like communal gardens, food forests, etc.

I think the best way is to grow a surplus of something yourself. Most people are shocked by how much of something can be grown in a few used plastic buckets.

I always get gifts of a wide variety of fruits, vegetables, preserves, venison and other hunted meats, etc when I'm out gifting fruits, vegetables, and preserves.

I've always got way more tomatoes, Nanking cherry jelly, raspberry jam (and fresh!), and crabapple jelly than we could possibly use. I just give it away, no strings attached. Most of it comes back in the form of string beans, cucumbers and pickles, Saskatoon berry jelly and pie, chokecherry jelly and syrup, salsa, onions, corn, etc. All of it comes back in the form of good will and general neighbourliness.

Over time, it's evolved into a pretty big community of sharing that goes beyond mere produce. Pick something, grow a surplus, and spread it around.

What is FNB?

But the only way I can think of to get the idea out there that people should share what they grow is to flat-out say, “you should share what you grow”

Have you tried the following?
"That would make great gift!"
"You don't have to worry about finding present idea!"
"your [insert family member from a different household]/neighbour must love them!"
"I wish I had such a production. I could give some to [insert charity] they always need some."
"Your friend must love you (^_-)" ~ Ok, that one is a bit rude, but you can reformulate.

People don't become in one day generous people that are open to give away and share there private property. It happened over time, starting with sharing within the most intimate circle and slowly spreading away until reaching strangers. Something like family>friend>neighbour>college>extended family> local community> anyone that could need it.

You could also mention how they could benefit from being part of community that share and how just a few people starting to share come make it possible.

If you're in an area with a lot of gardeners, maybe a weekly food swap would work. A place where people can bring their excess harvest to give away or trade for someone else's excess harvest. But you might end up with supply/demand problems (e.g. everyone showing up with too many zucchini and hoping to trade for tomatoes... and then leaving with too many zucchini and no tomatoes). Also, I feel like most excess produce is left unharvested, because harvesting it all would be too much work (especially fruit), or because it is kept around in the garden until it goes bad (I do this with radishes: I take a few every day until they become too pithy then in the compost the remainder goes), so people would have to be motivated and organized enough to harvest excess crops. And then you have the trade problem of making sure everyone feels they benefited from the swap and didn't get taken advantage of ("I harvested my entire fig tree and Sharon shows up with five maggot-riddled beets and that's supposed to be a fair exchange!?")

What you describe is at its core society's under-valuing land: a lack of recognition that arable land in particular is too valuable to society to be held by individual property owners to do whatever the fuck they want with it (including nothing, like using it for lawn, or worse yet degrading the land so it's no longer arable, like paving it or poisoning it with Round-up, garbage, etc). But changing that requires a fundamental shift in our perception of property rights that would take either moving to a commune of like-minded folks who intentionally forgo front yards for a community garden or whatever, or a major crisis like a famine resulting in the government's eminent-domain'ing of underutilized private property.

Sometimes it comes down to effort and people not knowing how to do things. We asked other market people how to run a stand on the farmer's market, for most people it's not common knowledge and there's no info online. It's not too expensive but not worth having the work, for the little surplus we have. Getting together with others to sell on the market is a solution we are studying, but that's already beyond what most suburban retirees are willing to do.

In your case, maybe setting up or suggesting an easy way to share surplus produce (public or private sharing box) can help, or setting up a group willing to collect and redistribute it (and give your gardeners the good feeling that they are supporting a good project).

Lend out tools and ask in return for a share of the harvest?