My parents is same as yours about speech and my house my rules thing too. But I got lucky get out of speech therapy only cos my speech therapist caught me cheating listening test and told me to tell my parents which I didn't and they never found out.
I had another problem trying to let my parents allow me stop wearing hearing aids. I had to take it really slowly, let them get used to idea, took me 2 years. Step by step like wearing one aid, etc.
I think you may have to be patient and take it slowly, some parents don't like to drop it just like that cos they feel like "I worked so hard for you to speak so well and is that how you repay me!". Is there any way to reduce length of speech therapy sessions? Like if you had 1 hour, reduce it to 45 minutes, then down 30 minutes, down 15 mins and eventually to nothing.
