How to use oleoresin capsicum (chilli extract)?
If you really want to, I suspect you can add it to oil to dissolve/dilute it before adding to your dish. I know you said you tried that, but it really should work if you mix the oil well (possibly with heating), and incorporate it well into the dish. If it still doesn't work, then perhaps the extract you have doesn't have the right balance of compounds.

But even if it works, at that point you might as well just use chili oil, or really any spicy sauce that you like. There are plenty that are hot enough to not need tons, and get your food plenty hot. It'll be less fussy to use, and less risk of accidentally throwing everything off with a drop too much.