How long can I hold brown rice between boiling and steaming?
You can wait as long as you need to between pre-cook (that's the simmering) and finish (the steaming), it's how things work in restaurants.

The steaming time will only go up if you let the temperature drop appreciably.  Even so, you shouldn't need more than an extra minute or so.  Steaming is pretty benign to rice.

As far as the safety concerns...if you keep the temperature above 135 F, you are out of the danger zone, and you can hold there forever.  The danger zone is 41 to 135 F, but the goal in cooling foods is to get it from hot to cool in 6 hours...below 70 in two, and then 4 hours to make it below 41 (yes, I'm ServSafe certified).  So your hypothetical 30-45 minutes shouldn't cause you a problem.  But watch it if you start going long.