Are you able to use a Target pharmacy? They are very accommodating. You can manage your Rxs online. You can set up auto-refill so the pharmacist refills without a call from you and when your refills run out they automatically call your Dr to update your refills. I get calls/texts letting me know when my Rxs are ready for pick up. Its pretty seamless.
The only problem I've run onto is when my T doesn't get back to them. If, when I go to pick up, my T hasn't called back they will call again. I will sometimes send my T a text letting her know they are waiting to hear and I am at the store waiting. Once they have the approval they can usually fill it within 20 minutes (there's always something to shop for at Target during those 20 minutes), unless they don't have it in stock which I have encountered only a few times in the past 10 years.