There shouldn't need to be any variation in the water at all, since the things that you are adding are already hydrated and are not taking in any water. Indeed, it would be possible that some vegetables might even give off water.
I would be more inclined to look to whether you are measuring accurately every time you use the rice cooker (just asking) and then, if so, whether your rice cooker is consistent. I had an inexpensive rice cooker that I liked for the convenience, but it was inconsistent on turning off, so the results were a little too varied, OK for me, but not when I was serving other people.
The only other thing to consider is that many rice cookers work on a temperature principle...when the temperature starts to rise (meaning the water has been absorbed) the cooker shuts off. If the ingredients you are adding are raising the temperature of boiling (as in a lot of salt, say) then it is possible that you cooker is shutting off before the rice is cooked, and then the water is absorbed or evaporates, but the rice cooks no further.
I would pay very close attention to your measuring (rice and water) for the next couple of batches and see if that fixes the problem.
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.
Best Answer
I use par-boiled long grain rice, and DO NOT pre-soak or rinse it. Put your rice into a good heavy based pan, add about three times as much cold water and bring to the boil, yes, you can stir it once or twice if you want. Boil for about a minute or two, turn off the heat, leave the lid on and wait about 30 mins (some times it might be up to 45 mins), the rice cooks very nicely. Strain and use as required. This always for me makes perfect fluffy non sticky rice - I have never had an issue with rice with this method. Of course this is for par-boiled long grain rice, other types of rice might act differently.