You are doing well... maybe you have same issue I used to have, here some precisions:
Unzip to the same directory as the mednafen executable:
Yes, you can just unzip the emu4crt.exe file to your existing mednafen directory.
At first launch, emu4crt.exe will add a new option to the mednafen-09x.cfg: video.UseNativeResolution (should be at 1 by default).
Mednafen save the fullscreen/window mode, so quit mednafen with ESC key while in desired mode, or have a look to the .cfg file.

If mednafen or emu4crt switches to a 31kHz mode, you can try this fix:
1 - Stop and Disable service: AMD External events utility
2 - Ensure that the Windows advanced display option is enable: "hide modes that is monitor cannot display"
This service often resets the "hide modes", so standard 31kHz video modes are exposed to applications, not good for our usage.
Switching emu4crt from Fullscreen to window is not dangerous, It doesn't create video modes on the fly as Groovymame, it can only use resolutions provided by Windows.
Just that the image will not be scaled correctly to 1:1 pixel but to a smaller or greater size. In such case you can wait that the game decide to change resolution.