If you’re doing low-carb high-fat, you might want to look into the keto-assisted protocol. We don’t have much info about this though but you can easily find FB groups that do the hCG 3.0 protocol which is Keto based – they may be able to help on this.
The original hCG protocol is low-carb low-fat low-cal, however, many ladies with PCOS have done the traditional hCG protocol just as it’s written and lost weight very well. The original protocols and modified protocols that are more closely tied to the original principles of low-fat and low-calorie have stood the test of time as far as working for most people – for a keto-style diet with hCG, there is not nearly so much evidence and it seems to be pretty hit and miss as working for some but really not well at all for others- but definitely if you have a lot of interest in it, utilize those resources to research it!