Rice is mostly made of starch. Starch is, in itself, a molecule made up of glucose components attached to each other. There are two types of starch: Amylose - it is a long straight chain of glucose - and amylopectin, which has a branchy and fuzzy structure. When you cook a rice which is rich in amylose, the grains stay separate. When you cook rice which is high in amylopectin, its starch molecules catch on each other and cause clumping. So the main factor is indeed the type of rice. While the amylopectin rich varieties in general are short grained and amylose rich ones are long grained, it can be that you accidentally picked a non-sticky short-grained rice.
Washing will cause less sticking. Normally, the starch in rice has to be released from the cells before it can stick. In a bag of rice, there are many cells which are broken mechanically during handling/transport, and their starch is free, clinging to the surface. If you wash it away first, you have less sticky grain so less clumping.
Now for soaking. Starches are packed very close in a grain. For gelation (that's when they cook and swell) you need both enough water and the right temp (70 degr. C). As heating is quicker than water penetration, presoaking makes things quicker. I guess soaking will help stickiness a bit, because there will be more molcules ready to swell in a short time. Plus, some of these will come undone from the grains and start swimming free around. This turns the water itself into a weak glue (so don' discard).
Using less water will help with stickiness. This will result in a bigger concentration of free starches in the water.
A slow simmering should also promote clumping slightly, as the starches will have more time to swell, move around, and hook to new starches.
All arguments above are the theoretical explanation for the direction in which the factors you mention are likely to influence clumping, given that the rice is always the same. In practice, their effect should be much smaller than choosing the correct type of rice. In fact, amylopectin rich rice types aren't soaked as often, because they don't need it - amylose is packed tighter. I don't know about washing habits, but it is cooked with less water, because it needs less. And any rice should be cooked slowly, a hot boil overcooks the outside and leaves the inside hard.
In the end, if your wife wants the rice she is familiar with, you must buy short-grain japonica rice. Else ask for a "sticky" indica, that's better than just eyeballing grain length.