Everyone above adding info is basically correct

I haven't given up yet though!
I've worked on modding this and I've also made an "official" request (
https://7daystodie.com/forums/showthread.php?111659-Scrollable-window-for-recipie-ingredients-optionally-also-scrollable-backpack ) to have the vanilla game modified to make the backpack and ingredients list "scrollable". For all I've been able to figure out, the "controller" in the grid area *or* the Window panel containing the ingredient grid is needed to be modified in order to handle the "scroll" effect, so it's not something you can change via the existing XML via a mod and have it look good/use able by others. I have 2 more ideas I'm going to try and if one of them is "use able" I might be able to increase the ingredient list to either 7-10 and make it visually appealing as well as work with all the various screen resolutions. I'll provide an update ( or likely a mod

) if I can get something working or if I fail.
How long this may take to get added to the vanilla game is beyond me but I personally consider it kinda a "modding bug" where they allow you to make mods and add items to ingredients and the backpack, but this specific case of "hidden ingredients" can make mods randomly "fail" badly, especially if a normal user just loads a bunch of mods up by different people and suddenly isn't able to figure why they can't craft something. Specifically: imagine that 2 mod authors test their mods and say "yes, I did not go over the 5 ingredient limit" everything works, but together the 2 mods add ingredients that go over the 5 item limit, "breaking" both mods.
I requested the backpack also be made scrollable because I looked at the backpack mods for some insight on how they did it and yeah, it "distorts" the UI by making the backpack slots very small. It looks like the "96 item" backpack is as many as can be added and still be sorta usable. If the backpack window scrolled, you could have a 1000 item backpack if you wanted (which would be kinda boring, IMHO) but if someone really wanted it, more power to them.
If you poke around the UI, almost all the windows are scrollable, so doing this in the vanilla game shouldn't be too much of a stretch, technically. It's likely going to be a combination of "they agree its an issue" and "they have time to do it over the actual bugs/issues"