For me the UI is a bottleneck too (notifications plz?) but I don't think that is a major player here.
I think it helps to learn to distinguish between actionable (or possibly actionable) posts, like security problems with products I or my customers use, “new” things that I might want to know about, and the other 90% of posts that have no relevance to me. If something looks actionable or interesting I read it and then maybe take action or write a reminder with the link, or save a bookmark.
So I do what you do: I just hoard tabs. Not just for HN, but for a lot of things I may want to read. Then I move on with my life. Some I eventually come back to read, some I don't. Either way is inconsequential to me and my life.
Shameless plug: If I need to track what I've read so far and to see new comments, I've made a chrome extension that helps me out with that [1].
I also do a quick scan for services, products, & utilities that I can leverage going forward. But they're rare enough, so it's not like I'm drowning in innovation on here.
1. I make it easier for me to determine if a link will actually be interesting or useful to me by using an HN interface that pulls forward additional information from the linked article/site to help me make a more-informed decision without having to spend the time of going to the linked article/site. I use Timbo's Hacker News Reader [0] for this.
2. I feel your pain about multiple open tabs. What I do here once I've decided I do want to read a link is I email it to myself, and I use an email alias in my email client of choice so I can search for these emails later. For example, I use the email alias "aaa" for articles I want to listen to later (i.e., "a" is for "audio"). In my phone and in my gmail client, the "aaa" alias is my personal email address but with "+audio" tacked onto the end of the name so I can pull those out later using a Python program [1]. I have another alias called "rrr" that tacks on "+read" and these are for links I have to read with my eyes, since they're probably heavy on images or have a lot of code snippets.
bonus part 3. The linchpin of this (or any) solution is that you have to make time to actually read the articles at some point. The problem of wanting to read more links than you actually are willing to make time for is a psychological one, not technical. It's like my other personal challenge of buying more books than I will actually make time to read. It's been a real balancing act to soberly decide whether such-and-such link or book is actually worth my time. Between work, family, and community, I have to be ruthlessly honest about what I do and don't have time for. All that to say, I think your question strikes at the heart of a challenge that many of us face and yet that many of us continue to struggle to resolve.
[0] https://www.thnr.net (disclaimer: I'm Timbo) see https://www.thnr.net/about/ for some of the info that gets pulled forward (like thumbnail images, name of social media channel, GitHub project programming language percentages)
[1] https://github.com/timoteostewart/benson (disclaimer: I'm timoteostewart)