I have a hard stop at three. — I must leave at three, and I will.
Got a sec? Do you have a minute? — May I interrupt you? The question comes before the interruption.
Let me find time. Grab 15 minutes on my calendar. — Let us book a slot. Or: book the slot yourself.
Send me an invite. — Make it a calendar entry, so that it exists.
I’m back-to-back all day. — My day has no open slot.
I blocked off the afternoon. — I reserved the time in my calendar, so that no one else can book it.
I’ll let you go. — I know your time is limited, so I am ending the conversation.