Hey Ross, I might have a solution to your problem.
There is a totally free software avaliable called Sizer (http://www.brianapps.net/sizer/) and was the solution to this problem for me.
Undertale without Sizer:
NOTE: there's no option to change resolution in-game
Undertale with Sizer:
As you can see, this program can change all selected windows in your pc to a proper size without blurring the image.
I'm also using the Sizer 3.4 Dev Build 482 that you can find here: http://www.brianapps.net/sizer/sizer34.html
You click once to open sizer.exe and it stays in the windows' task bar, as you can see here:
Now the first thing you are going to do after open sizer is go to "configure sizer" and set some resolution entries for different types of games/windows like mine:
i STRONGLY RECOMMEND, the ones that i'm using for windows (recomended to only 1080p monitors):
4:3 aspect ratio games: 1387x1040
16:9 aspect ratio games: 1849x1040
Full monitor: 1920x1040
4:3 (Bordeless Window): 1420x1065
16:9 (Bordeless Window): 1894x1065
Full monitor (Bordeless Window): 1920x1065
Now, I suppose you are good Ross!
Sorry for my bad english btw.
EDIT 1 08:50 (Brazilian DST Time) - 12/29/2015:
I made a video to show sizer running on Undertale:
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EDIT 2 09:08 (Brazilian DST Time) - 12/29/2015
Yes, If you tweak it in "configure sizer", you can make it run games in fullscreen. Note: I read somewhere that most of fullscreen games today are running in a bordeless window.
EDIT 3 09:13 (Brazilian DST Time) - 12/29/2015
Remember when i said: "I read somewhere that most of fullscreen games today are running in a bordeless window"? i found a source to it:
EDIT 4 12:32 (Brazilian DST Time) - 12/29/2015: I want to apologize to Spewkies. Sizer will not help with AA in emulated games.
Proof:
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I did this video to compare ZDoom and Sizer and this shows that besides of helping with the blurry problem, sizer don't mess with AA.
EDIT 5 13:40 (Brazilian DST Time) - 01/02/2015
BTW Ross, ALL my videos (like this) are in Creative Commons Attribution license 3.0, so you can use all my videos in your Birthday Follow-Up video (if you make a Birthday Follow Up video).