Indeed もうちょっとで~ところだった means almost, but I don't think the interpretation with a little more is wrong. (In fact, that's the original meaning.)
e.g.
もうちょっとでぶつかるところだった。
If I had run a little bit closer to it, then I would have bumped into it. = I almost bumped into it.
"もうちょっとで~ところだった is almost" or "~なければならない is must" is a way of learning, but I think eeky-san prefers the way of analysis "もうちょっとで is from a little bit more" or "~なければならない is from if I don't do that, the situation/event doesn't stand (so I must do that)".
I was in work, by the way.