I think this works:
Start with a construction that actually has too many rows (in this case, 20):
And then move one of the trees so that it breaks 2 of the rows but preserves the rest. In this case, I moved point A a little further out so it was no longer in line with the two sides of the red square:
Edited to add:
There is this, which is perhaps a bit prettier:
Or this pinwheel I made: