Hi again,
Regarding the degree of GPI, we do allow as high as degree 9, but as you said, we rarely recommend more than 3. Results very often get unstable and unpredictable when using high-degree polynomials. The curves will change direction one less than their degree (ex, quadratic curves bend once, cubic curves bend twice, etc), so a 9-degree polynomial will bend 8 times, and these bends can be unpredictable and not representative of the data.
If it looks like you need a degree higher than 3, we usually recommend using Kernel Interpolation or Local Polynomial Interpolation. It is usually better to build low-degree polynomials locally than it is to build high-degree polynomials globally.
However, these are just general recommendations. If there's something about your data where a high-degree global polynomial works best, you can of course use it.
-Eric