Are you counting 5-8 minutes to heat water + 5 minutes parboiling the rice + 5-8 minutes to heat fresh water? If so, you’re double-counting one of those steps, because you already have to heat water when cooking rice. Using your figures, the overall cooking time would only increase by 10-13 minutes.
You could reduce that to ~5 minutes by heating your cooking water during the parboil step, rather than after, so it’s ready to go when the parboil is done. In a kettle or second pan, for example.
You could further reduce it to <1 minute (the time it takes to replace the parboil water) by taking 5 minutes off the cooking time, since the newly added 5 minute parboil is cooking.
I hope the fediverse doesn’t cook meals one step at a time. That would take ages. :)