Would I be able to "jump-start" my rice cooker by pre-heating the water on the stove?

that would work, but at that point I would just finish the job on the stove

I think you need a new rice cooker! A good one should be faster than preparing rice on the stove.

I do… it’s a top-of-the-line zojirushi!

On the subject of rice cookers, mine has a no stick surface but the rice really sticks badly no matter how much I rinse it before I cook. Seems to make a gluey mass on the bottom, any ideas???

try using a table spoon of vegetable or olive oil.