Based on ASA (and most other, if not all) rules, you have it exactly right.
By rule, R1 cannot be put out (by the defense) between the bases where she was obstructed. In your scenario, that's first and second.
When F6 throws to second for the force out on R1, an obstructed runner has been "put out" by the defense between the bases she was obstructed. This is an immediate dead ball. Award R1 second base, because you can't send her back to first. BR is awarded first base.
In this case, your judgement about whether R1 would be out or safe at second does not matter - the written rule takes precedence.
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