I've had success in the past with this "uninterrupted time" problem by first giving a little explanation - nothing elaborate, just stating facts, and setting a visual signal as a reminder. Something bright and different than usual in the foreground so it's seen first.
Maybe an orange traffic cone, or a piece of construction zone tape across the opening used to get to me.
That was a solution for me professionally.
At home I found that if the persons interrupting were told I'd give them undivided attention later, ie make an appointment with them, and I kept it as promised, and really did focus on them as they interacted with me it broke their pattern of feeling they had to interrupt me to reach me and be heard.
It does take a bit of time up front to get them "trained," but ultimately it not only really did save a good deal of time it vastly improved my relationship with them.
It's respectful and gives the message that you think, by demonstrating, they are important too.
Sometimes it works nicely with horses.
I guess I need to reinstitute this with Bonnie. She gets terribly cranky and upset, bucking and squealing in her stall, even kicking the wall occasionally, if I attend to Altea first. Hmmmm...maybe my advice was really meant for me rather than you. In fact you probably had this worked out long ago.