You can map your UVs to a smoothed version of your polygon model, where it may be easier to get good UVs (for example, you can smooth out wrinkles which cause overlapping UVs). Then you can use the Transfer operation to copy the mapped UVs back onto the complex original model.
To transfer smoothed UVs between polygon meshes
The higher the value the more smoothing. You can click Apply repeatedly to smooth repeatedly.