First, in what language are you very good at writing? How this will be perceived may vary from culture to culture, so that’s an important factor to take into account.
Second, while it’s true that most games have little or no moral content, I don’t think it has to be that way. You’re smart to plan a low budget for this, especially if it’s a short game, but I would say go for it — if you can make it interesting and fun, players will forgive the moral lesson.
I was having somewhat similar thoughts yesterday… I’ve been watching a lot of Japanese dramas lately, working on my language comprehension. I seem to be drawn to high school stories (like GTO and Back to School at 35) for some reason. The stories in these are pretty formulaic: our hero stumbles across some poor student with deep problems — bullying, self-injury, domestic abuse, caught up with the yakuza, fallen out with their best friend over some ironic misunderstanding, whatever. The victim is almost universally hiding the problem and unwilling to admit or face the real issue. And then, through unconventional and highly dramatic means, our hero forces them to confront the core issue, at which point all the troubles evaporate and they become well-adjusted, happy young people again.
It’s all very sappy and predictable, but it’s darn fun and I can’t seem to stop watching it. My thesis on fun is that it’s fundamentally about accomplishment — and to me there is a much deeper, more satisfying sense of accomplishment from helping out somebody who’s in trouble than there is from, say, killing aliens by the hundreds. (Of course in a TV show this is a strictly vicarious sense of accomplishment, but it still works.)
So, I’ve been wondering whether/how you could make a video game around the same kinds of plots.
I don’t have a good answer for that yet… but it sounds like you may have some ideas along similar lines. I say give it a try, and see if you can find the fun! Give the player some real choices, and make them feel they’ve accomplished something important (even if only on a personal level), and you may have a winner.