Thats a pretty good system that you describe there Ghenghis. I assume the aircraft is the equivalent of the old public transport regarding maintanance and engine life in order to be leased into the club?
The OP is of course going to have the problem of finding a club as enlightened as yours that will allow effectively a competitor to the club and its instructors under the blanket of the clubs approval. I would not let you do what you describe under our approvals as I could not be assured that you would meet our standarisation and quality requirements but as overseeing CFI I would still be responsible for you. You will find a lot more schools that will give you the same answer. As they will basically see you trying to ride on the back of their approvals without having done the legwork.
To the OP, don't underestimate the responsibility and difficulty in teaching ab-initio as an inexperienced instructor. It is probably one of the most challenging things that you will encounter as an Instructor and you will benefit greatly from the oversight of an experienced CFI and being around other more experienced Instructors.
AS I said earlier, get the experience on the staff of a school and get the restriction removed then spread your wings. Once you are unrestricted you will be in a position to start your own RTF and do what you want.