Then I decide, hey, no, I don't want to send that message anymore, I want to send something else. So I interrupt the blinking.
Does that appear comprehensible?
Yes. You have not written your program that way, though.
Once you have defined a string to send, it sends the whole string without the ability to interrupt it.
Perhaps what you want to do is to collect the string to send, when there is serial data, and then send one character per iteration of loop(), outside of the if(Serial.available() > 0) block. That way, you would not have to wait for more than one character to be sent, before the arrival of more serial data interrupted it.
You could even have a start marker that caused the new serial data to be appended to the current message and another one that caused the serial data to replace the current message.