I know you're looking for out of the box thinking, but too many marketers obsess over thinking outside of the box and they forget the basics. In this case, you need to pay way more attention to the 'simple' things.
Idea 1 - > FYW (Fix your website). On mobile, your website is a mash of horrible alignment and weird word wrapping. I use Safari on a fully updated iPhone 5c - if I'm having problems, so are others. Based on your website, you couldn't pay me enough to become your customer - I can't trust your ability to format my message if you can't even format your own website. Online marketing is really at least half QA.
Idea 2 - Within a second of loading your page, I got overwhelmed by how quickly {Name I have never heard of} will Email you Five tips about {something I can't see because it changes too quickly. Fix that.
Idea 3 - Work on your copy. Between your Ask HN text and your website I have no idea what your service really does or how it will help me. And, unfortunately, the quality of the writing on the first page keeps me from subscribing to any newsletters. If you're going to highlight content, it needs to be good. I don't need more poorly written articles on growth hacking and I will never engage with that type of content.
Idea 4 - Are you really solving a problem? If so, whose problem are you solving? Go talk to those people. Personally, from what I have gathered from your site, I think this was a problem that I had eight years ago.
I understand that there is too much material for me to read and I know that discovery is a problem, but if you're concerned about customer acquisition, you need to prove to me that your solution is better than my solution. Therein lies my point about paying attention to fundamentals.
Sorry to pick on one writer, but one of your mailing lists is advertised as, "a collection of new tech ventures that are worthwhile watching." Another is described as "News from accelerator world." Not only do those contain pretty severe grammatical errors, but they don't exactly make for a compelling call to action. Why would I subscribe to lists curated by people who can't even craft compelling intros? I know that writing intros is hard, but poor intros don't exactly fill me with trust about the quality of the links I will receive!
If this project does what I think it does, you're going to run head on into a chicken or egg problem. Nobody will subscribe unless you have amazing content to send out. But nobody smart enough to consistently send out amazing content will spend time crafting amazing content unless there are users there.
Once again, focus on the absolute basics before you start thinking too far outside of the box. In this case, you need some extremely compelling content on your first page and that content needs to be so good that I can't imagine leaving without signing up.
Idea #2: Go talk to your curators, or whoever you think will be your curators.
Your questions above point to the fact you are trying to solve your problem (how to get customers), rather than your customers problems.
What does "more engagement" look like? What behaviors denote "more engagement"?
Once you talk to 10-20 curators you should have a solid understanding of what "more engagement" means to them.
From there brainstorm possible solutions that will effect that.
Rank your solutions on a graph with Bold - Not Bold on one axis, and Likely to Solve - Unlikely to Solve on the other.
Create experiments starting with the most bold and most likely to solve idea.
The boldest, most likely to solve idea that subscribers and curators are willing use will probably be innovative and better define your UVP.
Ask your curators if they had any specific ideas for engagement and see what the subscribers think about that.
You've got to be your product's non-technical founder, and coordinate with your users and customers to build what they want.