It took me a while too; it can definitely take some time until you find a flow that works for you. For me, what I do is that I actually quickly switch between the speakerbox and taking care of the person at the window.
“Hi there! It’s $5.66 whenever you’re ready.”
“Thank you for the choosing Starbucks, what can we make for you?”
I process their payment and hand out their order while I listen for their order.
As I finish taking their order, I’m already sending off the person at the window.
“Okay, what else would you like to order today?”
“Thank you, have a great day!”
“Alright, we’ll see you at the window for $6.08.”

Don’t feel too bad if a coworker picks up the order for you; I take it as getting support. It’s stressful at times and inevitable that you’ll have to slow down when your flow is broken. It’s important to take difficult situations in stride and try to keep a flow up and running. Don’t be afraid to tell customers that you need a second because you had a question at a window if you need to slow down; and sometimes it’s good to signal in other coworkers when you need it so that you can keep that drive line going.

Just make people wait. I do both Almost every time I work now. Just do payment then say your drinks will be out soon. Then take an order and just keep doing that.

My advice first and foremost is to let your SSV know you need people to stop picking up because it’s not letting you establish a pattern to be successful in your role. When I do both, as soon as I hear the ring (or as soon as able of course if your customer at the window is in the middle of speaking) I tap into the microphone and say “Hello there! I’ll be with you in just a moment, sorry for the wait.” And finish the window or if there is a gap of time before their order is ready after taking payment, then I’ll go back to DTOing until I’m done with that customer and return to finish with my window customer. If there isn’t a break after taking payment at the window before the car’s order is ready, as soon as I get those people their purchases I close that door and get back on the mic for Dto so those people aren’t waiting too long.

This all being said, in order to do both roles successfully you need to have someone who can do any food you don’t have in grab and go or warming items, and bar partner has to collect coffee and tea if it’s busyish. Otherwise, your going to create wait at your window just because you are taking on too much of the workload.

Also! If you have a strong bar partner and they are close to your dto screen, establish a rhythm where you can ask ahead for them to type in your order if you do have to run and grab your oven or food items. But that’s worst case scenario.

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Let them know that’s not cultivating the Starbucks experience. How many partners do you have on shift? And what day part are you having to DTO and DTR?