How can I make regular rice more sticky?
Those are all good ideas, and will work together.

For "use more water", what you really want is to use more water but not end up with wetter or softer rice. (For rice I want to be sticky I'll generally use about 1.25 volumes of water to one volume of rinsed and drained rice, but this will vary widely with cooker and amount of rice.) A good way to do that is to stop cooking after the prescribed length of time rather than when your rice cooker detects that all the water is gone, and then spread the rice out on a plate immediately after cooking, to promote evaporation. (You can also do stuff with stirring and fans - check out videos of preparing sushi rice - but it's probably not necessary.)

I've never gotten rice to be sticky if made with stock or any sort of fat.

Long grain rice won't be as sticky as short grain rice, but it won't be far off either.

Finally, if you just want to cheat, sprinkle some rice flour in with the rice. Like not rinsing, but arbitrarily moreso.