Writing my speaker's bio when I have very little relevant experience
Don't overthink it. It's true that people will be attracted towards some talks because they are given by a "big name", but it's also true that people will also base their choices on the content, regardless of the speaker. The majority of attendees, if they see a talk on a topic that is of interest to them, will not turn it down just because the speaker has an unimpressive bio. In fact, I suspect many people don't read the bios at all, certainly not all 250 words!

I would recommend a cross between 2 and 3. Give a brief mention of your previous work, because it's a part of your background, and if nothing else, people like to know about the different career paths that others have taken. Then perhaps describe why you moved to your current role/area (avoiding phrases like "filling a mundane role"...), with an emphasis on what you find interesting about it and any ways that it links with your previous experience. That should allow you to talk a bit about the project while still keeping it relevant to you personally. You can keep it fairly brief though - don't feel like you have to use up all 250 words just for the sake of it.