...when I try to use some of the System Settings payloads (for settings that do not seem to exist in Jamf), the payloads disappear when I upload the .mobileconfig file.
I think what you're experiencing here is exactly what you described. These settings don't exist in Jamf, but because Profile Creator is using one of the actual profile payloads for the OS, when it's uploaded to Jamf, those settings don't appear, at least in the GUI. However, have you tried pushing one of these uploaded profiles to a system to see what gets applied? It's possible that the settings are in fact in the profile but just can't be shown in the UI. You should be able to see all the settings in the profile in the Profiles preference pane once it gets deployed to a machine. If it's there, then you'll know it's all good, but you won't be able to visually see them in the UI.
If that's not acceptable, then the only other option might be to use the Custom Settings payload and upload specially crafted plist files, assuming the settings you're trying to apply can be written to plist files that is.
Edit:
@sdagley & @tlarkin - from the OP:
I have tested this with both signed and unsigned profiles.
Seems she has already done what you suggest. I think the actual issue here is that Jamf can't display items in profiles that it doesn't specifically know how to manage.
An example of this: you can create a profile in Profile Creator that lets you manage some Safari settings, like the HomePage (though it doesn't seem to work reliably) and the behavior of new tabs and windows, as a simple example. Whether the profile is signed or unsigned, when it's uploaded to Jamf Pro, what you see is a profile with just a General payload and nothing else, because Jamf doesn't have a Safari payload option, so it can't actually show it. However, if you push the profile to a Mac, the settings get applied (usually) and show up when viewing it in the Profiles pane in System Preferences.