Occasionally I will stumble upon a web-based game that reminds me of a PBM. Take a look at Prosperous Universe. It's a space economics game. After you get everything setup and running, including the customization of the user interface itself, you log in 5-10 minutes a day to manage things. The game moves slowly (which I love), so don't expect immense wealth and power to come swiftly.
It's under active development now, and many new features are being added. It has one of the best user interfaces for a web game I have ever seen and allows full layout customization.
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Have you tried playing yet? I would definitely count this as a PBM-like game. I love the screenshots, and the idea. Any reviews you can share?
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I am playing it, although I don't have any more access codes to give away. I think it's a small fee to join right now in pre-release. The first week or so was amazing, then it settles into a bit of slog. They are still adding a lot of features, so I expect it will improve quite a bit.
Carbon Farming is one of many ways to start. Based on what I know about you, I don't think you'd like Prosperous Universe. It seems geared toward CPAs who wanted to be Astronauts as kids.