Runner hit by batted ball

[tarheelcoach]

Here's a situation that occurred last night in a Dixie tourney game.
Bases loaded, one out. Batter hits a grounder that strikes R1. 1B was playing behind the runner, and it would have been an easy play for 1B. U1 immediately signals the runner out and calls the play dead. That much everyone agreed on. The question arose about what to do with the other runners -
1.) BR takes over at first, the other runners remain at their bases.
or
2.) BR at first, R2 to third, R3 scores.

The Dixie rule reads:
The ball is dead and no runners may score, no runners advance, except those forced to advance.

That last part is what is confusing. Does the interference by R1 take off the force?

We used the second choice, allowing the run to score, and the head umpire later said we did the right thing, but I'm not so sure now thinking about it.

What is right?

Also, U3 stated the play should have been live. The Dixie rule clearly states that is not true. Is there any rule set that allows the play to continue when a runner is out for interference?

Just a former coach who is now learning to umpire (no clinics yet, will do some in prep for school ball next year.)