The moiré effect becomes an issue when the sharp outlines of pixels from the projected image interact with the texture of the screen in such a way that areas of light cancellation occur due to phase changes in the reflected light. The defocusing trick works because the reduction of the hard pixel edge causes a more random scattering of light which cover up nodal interference. You can verify this by placing a smooth, white sheet of paper on your screen and watching the moiré pattern disappear in that area.
So, how to fix it? A reduction in the light intensity may help a little. Overscanning or underscanning the image might also work. A geometry change is also another idea. Try lowering or raising your projector, or tilt it up or down if you have vertical lens shift and keystone it (which serves to underscan). The best solution is to use a very smooth screen texture, or upgrade to 4K on the projector side but those aren't cheap fixes.