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.