I did some research on the subject and theoretically you should be able to insert
<key>LSUIElement</key>
<true>
right before
</dict>
</plist>
at the end of a .dmg file to get the icon to hide from the dock even when it is in use. I'm not looking for a workaround like "Change the dock icon" or "Just hide the dock entirely" or something like that, I'd like to know how this sort of thing works and why it is just crashing the application rather than hiding the dock icon.
I figured it out, LSUIElement apparently just crashes some applications, but a workaround that performs the same thing is NSUIelement instead of LSUIelement. I love that I spent hours researching this and then found the correct answer 2 minutes after asking.