extract the file from the removed apps ZIP and move it in the system/app folder of the ROM zip file before you install the ROM
should work till i find better solution for this.
Yes, I did this. I even did everything again from scratch: copy apk files to the /system/app of the Zip archive and flashed again - same problem.
Seems that the only possibility is trying to extract the LG Weather Widget and other LG apps from another image using Titanium Backup, then flash your image and restore the apps...