To me it's not a "attract them" problem, it's a "keep them" problem.
I know that I've long considered myself a UU "irregular", which makes me "part of the problem". I show up as I feel like it when the whim hits me or there's a lecture/speaker I want to hear that week or I generally just feel a need for some coffee with a group I know I can typically count on to socialize with. Without the implicit coercion of "traditional" services have behind them telling people they must show up every week, UU can be seen as having a bit of a disadvantage on that front in keeping/maintaining/growing their communities over time. (The little UU church that is my favorite in my hometown is not quite 150 itself yet, I don't think, but probably shares a lot of similar tales of growth and shrinking over a nearly as long of a lifespan.)
At that point, so far as my advice may be, for what little it might be worth, finding repeat visitors that become irregulars that become regulars are a marketing problem like just about any other social club or an MMO videogame. There probably are things to draw from some of how those cope (or don't) with very similar problems. Help people feel welcome, help them feel engaged, help them find reasons to keep coming back.
That's a nice phrase, and it seems to describe be at the moment as well.
The UU Churches are often very focused on their socialization side, with an old joke being that the UU sacrament is the social "miracle" of turning water into coffee.
There are a lot of more secular/atheist attendees of UU churches and UUs tend to embrace the diversity and the spectrum of beliefs. It's not a bad idea to give your local UU church a try if you haven't already.
[1] The interesting history of it is that both the Unitarians and the Universalists (once different groups) split from the mainstream Christian churches surprisingly early and relatively much more quietly compared to the Protestant revolution. The Unitarian dispute, especially, dates back the Nicene Convention that resulted in the Nicene Creed still central to modern Roman Catholicism and still often referred to by Protestants as well, although the organized church is quite a bit newer than that originating dispute in which the Trinitarians won the orthodoxy; UUs will tell you've they've been bucking orthodoxy for centuries.