Do you have any tips about making the pudding ahead of time? It looks like I can do the rice milk ahead of time, but what about the pudding?

Restaurants do indeed often partially cook food to be finished later, but they also have blast chillers at their disposal to rapidly get the food below the zone where bacteria multiply rapidly.

Ones that do this and don't have blast chillers end up making people sick.

If you cannot do the dish right before serving, cook it all the way and then refrigerate. It won't be the best it could be, but it won't put you in the hospital either.

A restaurant would cook the rice pudding to about 75% doneness and dump out onto a parchment paper lined sheet pan for rapid cooling to stop further cooking. They would then finish it off to order.

This is how restaurants also do risotto and similar dishes.