This situation is a major challenge for you. I'm glad you are thinking it through before you take any action.
Before I was licensed I interned at several clinics. I received both individual and group supervision on a regular basis. Group supervision was very helpful because we addressed the system of the clinic as well as client therapy issues. They go together as you so eloquently describe.
As I know you appreciate, many different forms of therapy exist, forms that come from different and sometimes conflicting philosophyical bases.
You seem to need clarity about your supervisor's therapeutic base and the main treatment philosophy of the clinic. Then you will have a better way to understand where and how you are in agreement or in conflict with your clinical environment.
Once you have that clarity you can decide if you are in the right place for you.
Question to ask yourself:
Can you work within the treatment philosophy of your clinical environment?
Your answer, yes, no, maybe, determines your choices.
Stay, leave, introduce desired change, experience more regular supervision with your supervisor in a group so different perspectives get aired, explore other clinical settings that are more in keeping with your work preferences, consult with professionals you respect in the field to explore options.
Also, and this is such a sensitive area, can you explore within to see if any unresolved countertransference issues are coming up that affect your vision?
We work in what is called "the impossible profession." Looking without, within and at the transitional spaces is never easy, especially when our emotions color what we emphasize.
Any supervision you get has to take into consideration the culture and philosophical base of the clinic.
If it doesn't you might not be to implement suggestions. Some clinics are eclectic and offer many different therapy styles to clients. Others do not.
Please be clear about where you are and what is honored in your setting. Then you can make more clear decisions about your next move.
I hope this helps, Shh.
2. Do you see a possible way to introduce change?