Using Random Forests as a GAM

This is a regression problem. I have a dataset of sales of various products overtime. I have three kind of feature sets : Price features, Product features and Seasonality.

I want to build a customer estimator which is defined as follows : y = a*price_features + RandomForest(Product features + Seasonality features).

Moreover if there would be a possibility to switch RandomForest with some other non linear estimator it would be even better.

So the model is linear for price features and non linear for product and seasonality features. How can i do something like this in python ? I am interpreting this problem as GAMs because I express the model as a sum of Linear and Nonlinear components. I know that GAMs are fitted using backfitting but i dont know if I should take the pain of writing the whole backfitting algorithm. Also i am pretty sure there isnt a package which provides the functionality to use RandomForestas a GAM. I would really appreciate some insights. Thanks