Browser used wasn't mentioned, but one idea would be: assuming your browser has a Zoom mode (Chrome does, Firefox does, etc.): see if there's an extension/plugin/addon for your browser that allows Zoom to be set on a per-site basis, then set forums.nesdev.com to 90%. Yes, the font/everything is going to be 10% smaller, but it should suffice.
There's really no "fantastically clean" way to solve this problem server-side other than doing a whole bunch of patches to phpBB -- patches that have to get reapplied by hand every time there's a phpBB version upgrade (and likely won't patch cleanly between versions, i.e. you have to re-do the work every time). For a while we had to do that on nesdev to get UTF-8 support working (I think patches were provided by Quietust? I forget), and every upgrade was a cross-your-fingers-grit-your-teeth experience.
One feature I do wish phpBB had was letting a user toggle the "Last visit was / It is currently" line at the top of the page. It's
<div id="datebar">. That div and underlying table takes up 16 vertical pixels of space. And that gets me thinking:
You might be able to achieve what you need through an extension/plugin/addon like Greasemonkey that can let you "tweak" HTML or CSS content on a per-site basis. For example, it would allow a person to do something like
div#datebar { display: none } while not having to change anything server-side. There are probably other extensions that can do this too, but Greasemonkey is the one that comes to mind, though it usually requires that you know Javascript.
Off-topic, sort of: reality says your "web experience" is only going to get worse as time goes on. It's not just you though, nocash. It's a horror I'm going through too, now that more and more websites are adding large amounts of padding and increasing font sizes in their UIs. I've asked front-end folks why they keep doing this and the response is always the same: "it looks better on 4K monitors". Yes I'm sure it does -- and for the 90% of the world that is using 1920x1080, 1920x1200, 1680x1050, 1280x1024, or the still-insanely-common-on-laptops-and-I-don't-know-why-we-had-higher-resolutions-in-the-early-2000s 1366x768? "Sorry, you're screwed". What webfolks don't seem to understand is that for technically-inclined people, we prefer our screen real estate be used up by display of actual information, not empty space.
And FWIW, my second monitor is a Dell E178FP (17" @ 1280x1024, VGA). It's ancient, but better than nothing. My primary is a 13-year-old Dell 2407WFP (24" @ 1920x1200, DVI) that's literally dying as I speak. In other words: I empathise.