I'd cook it in a regular sauce pan, I guess you'll need a big one for your solution. Then add whatever additives you want (rice vinegar, Mirin ect). Then wrap the rice you're not going to use in cling film like onigiri and place in the fridge for the next day. This is a standard method for Japanese people who take lunch to work.
There are big rice cookers but unless you can rent one somehow (Japanese caterers perhaps?) then it'll cost you a couple hundred at least and you have potential problems with voltages and the language difference.
Definitely do not add oil or butter, I tried a similar thing once and it ruined the rice. Fat and Japanese rice do not go together.
The bigger issue are the dishes you are preparing the night before. Unless you wrap it in cling film it'll dry out also for sushi/sashimi you really should make sure it's fresh off the boat the morning it is served and never warms up.
There is a couple of possible reasons I can think of.
Over stirring the mixture could be breaking the rice down releasing more of the starches which will be making the sauce thicker and sticking the rice into clumps.
Over cooked rice again making the rice overly sticky.
Like you've mentioned, lack of liquid. If the sauce is getting far too thick the starches will be more concentrated again sticking the grains together.
If the sauce is thick then certainly adding more water should help loosen it up a bit. Soaking the rice in cold water for half an hour before and then rinsing a few times will help get rid of some excess starch.
Also a possible factor is your choice of rice type. Some are more "sticky" than others.
Without tasting it myself it's hard to give a 100% reason but hopefully you will get a better result by paying attention to all the above.
If after all the above methods one last ditched effort might be as follow. 12 years ago when I was just starting out in my first kitchen I remember my head chef telling me "when you pour you're rice into boiling water, you must make sure they all fall freely and hit the water individually". Now I've remembered this ever since and thought about it every time I've cooked rice since, I've never done it though and can see NO reason why it would work or make any difference.
It's also worth noting I've never used a rice cooker in my life, not even sure what they are or do...
Best Answer
You can replicate a Thai rice steamer with a deep frying pan, a splatter guard, and a heatproof bowl. Just place a mound of soaked glutinous rice in the centre of the splatter guard over simmering water, then place the bowl on top, and steam for about 20-30 minutes, turning the mound over once or twice to ensure even cooking.