Okay, I reread and came up with a similar idea to my last one with some adjustments.
Pour a cup or two of wine into a sauce pan, juice your fruits, add the juice along with sugar and reduce to a thick syrup.
Take all culinary vegetables (ie., zucchini and tomatoes are botanical fruits, yet culinary vegetables) and tubers and begin to grill them, flipping them much more frequently than you would if you were able to oil the grill. Being a vegan cook, I don't really see the chicken fat as an option for oiling the grill, especially since it's been mentioned as "undesirable". If available, the vegetable can be grilled in some aluminum foil in which a few holes have been pierced to allow some smoke in. This may also help retain some of the moisture of the vegetables, which they will lose if they're out open on the grill.
As the vegetables cook, slather some of the reduced syrup onto the vegetables and allow the syrup to cook on. As the syrup cooks on, keep adding a new layer of syrup until the vegetables have cooked to the point that they are nice and tender.
The zest of any citrus fruits can be sprinkled on as a seasoning once the vegetables are done cooking.