I taught myself web design several years ago but I haven't kept my skills up to date, that stuff changes so fast. I think in the early days it was easier to break in, but now with so many easy to use website builders, many people are able to make a good-enough site on their own, so basically you're left with nepotism like you mentioned, and that's why I never pursued it.
With an economics background, you could easily offer services (at least here in Cambodia) to Microfinance companies here, possibly even major banks. Perhaps specialty English classes for the finance sector could give you a backdoor into other types of work within the industry. Once you're foot gets in the door I could imagine it would be easier to find more ideal jobs and get away from teaching.