Counting The Run

[CecilOne]

Able is on third base and Baker is on second base with one out.
Daniel hits the ball on the ground to the shortstop, who scoops up the ball and tags Baker out.
When attempting to throw the ball to first base, the shortstop is interfered with by Baker.
At the time of the interference, Able has reached home plate and Daniel has reached 1st base.
Assume the throw was never completed, no play at 1st.

My opinion: Daniel reaching 1st before being out allows the run to count.

Questions:
1) Does the BR being out as “closest to home” occur simultaneously with the INT?
2) If so, since with a dead ball nothing happens, does that alter the run counting if INT occurs before the BR reaches 1st?
3) Does a BR being awarded 1st on the INT change the ruling?

Comment based on any rules, but please specify.