Hi Anita. It's always a pleasure to see you on the forum!
I've sent out customer satisfaction surveys using surveymonkey (free for up to 10 questions). I agree that allowing clients to give feedback in their own time allows them to give more honest and precise responses rather than just a general "everything's awesome" over the phone. I am also mindful of keeping the survey reasonably short as my goal is to save my clients time not create more work for them.
I sent mine for many of the same reasons. I wanted to know how I was doing, what's working, where I could improve, and other ways that I could help them. It's great to get their perspective on how everything's going.
I've played around with including a request for a testimonial and referrals on the customer satisfaction survey and also sending it separately at a later date. Both worked well with some great responses.