Since this is mostly a UI improvement attempt, I guess you're basically just competing with https://news.ycombinator.com/show?
My biggest issue with this approach is it seems like a "poll" of arrows isn't really going to give enough useful feedback to be meaningful. If I've taken the time to actually review a Show HN, I'm not going to skimp out on the feedback phase by using a 1-click option. I'll probably have 3-5 paragraphs to write out.
Psychologically, it seems a bit rude to leave just a down arrow on someone's best effort project without explaining it. An up arrow alone seems fine. Of course, HN already has these built in.
If you want quick-hit feedback, can you also include a textbox for typing a quick note in addition to the short reasons already there?
A popup bar alerting about cookie usage is extremely off-putting to me and was almost enough to get me to just close out of the site before doing a review. If there is anything you can do to stop using so many cookies that you need to warn users of them....
The entire list isn't that long, can you get a deeper backlog? The /show page lists them chronologically which seems pretty nice to me since then a DevelopmentKitchen user can always pick up where they left off. You're currently sorting them some other way and it doesn't quite make sense? If I'm going to use JUST this site to monitor Show HNs, I'll want to know which ones I've seen and which I haven't.
Good luck!