Here is roughly what Basilio said:
He said that Dooley knows, that Hart is essentially keeping him as the interim coach, that Dooley has a choice to keep his head down and tow the line until the end of the season, or quit (presumably giving up on the payout), and that he thinks that the boosters are going all out with Gruden, but that there is a list with several impressive names on it.
He said that he wished it would happen now for the fans sake, but that everybody should be patient and that good things are happening. He did not hold back on Dooley at all.
If, and that is a big if, he is correct, then it may make sense to let Dooley finish. If they think that they can get Gruden, but not until after MNF, then why pay Dooley to sit on his couch when he can at least run the show until then? Maybe Dooley gets tired of it and quits sooner.