Just a few ideas that come to mind here - first, I wonder if the black walnut tree needs to be more mature to start secreting the alleopathic agent (juglone) through its roots. Maybe you've prevented it from spreading the stuff around by picking up the leaves and fruit, but I'm pretty sure they also secret the stuff from their roots. Second idea, it's possible that your three other mature plants, the rose, baptisia and lilac have deep enough roots that they haven't been affected by the walnut tree yet. No idea about the tomato, but there are some plants that are tolerant of growing near black walnuts.
Unless you're able to talk your neighbor into having the tree removed, I think your only options are to keep doing what you're doing, picking up the "droppings" and to prune the tree as much as you can on your side of the property line and cut off the flowers, too. They also have the juglone in them.
Here's a good article I found, with a list of plants tolerant of juglone:
http://www.mortonarb.org/trees... It specifically says that baptisia is NOT tolerant, so if you can't remove the tree, I'd think about moving that plant asap. It also says that tomatoes are not tolerant, too . . . so this again indicates that the roots of your tree aren't affecting the soil much - at least not yet.
Wouldn't your climbing rose also be a lot happier growing in more sun? The tree must be shading it quite a bit. Very hard to move an old, established one like that, but maybe think of starting some cuttings of it in case the walnut does poison it down the road. It may be an "own root" rose in which case the cuttings will come true to the original plant.
