The current answer I am leaning towards is:
-Respond to applicant;
Hello NAME
Congratulations on your other job opportunity. I will not be able to confirm an opportunity with us before the end of this week. I expect to be able to let applicants know NEXT FRIDAY, ##/##/##.
I understand this might be too late for you. If so I wish you all the best and encourage you to apply again in the future if you are interested.
Kind regards, ME
And leave the interview process as is and accept that some good candidates will get multiple job offers.