I had the same problem, but I only really worried about it in my veg area (which was anyway the most pouplar part of the garden as the soil was kept tilled). I tried all sorts but nothing worked and I ended up buying a roll of weldmesh about 100 x 100 and made cages to fit over my 4 foot wide veg beds. It did the trick perfectly, although the cats went to other parts of the garden which weren't suitable for the weldmesh (which was a bit unsightly and a little bit of a hassle, but better than s*** on my fresh veg and seedlings dug up or buried). I too prefereed not to fall out with the neighbour.
In your (floral) situation, I don't think you can win.



