[CecilOne]

Sorry, I have not been able to get back to this, in spite of some good points and thorough comments.
My intent in posting this was a good "drilling down" discussion of the timing aspects; which all did with several good points.
Sure, hypothetical about who reached which base at what time, especially Daniel reaching 1st before the INT, and whether SS had a play or not.
I visualized the Baker and SS play near 3rd, allowing some time for Daniel and Able to run. That also ignores why the SS did not throw to HP.
SS having a play was assumed in the OP, without specifying why.

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

Questions:
1) Does the BR being out as “closest to home” occur simultaneously with the INT?
We agree that it does.

2) If so, since with a dead ball nothing happens, does that alter the run counting if INT occurs before the BR reaches 1st?
Making the BR is out before reaching 1st?

3) Does a BR being awarded 1st on the INT change the ruling?
My point was that if a BR is awarded 1st on another runner's INT, the BR has by definition reached 1st safely. If so, that would allow the run to count, regardless of where the BR was at the time of the INT.
The BR would still be out as "closest to home".
I can't tell if anyone really agreed or disagreed.