ADB to the rescue once more. You can do 'adb backup -noapk indivi.indivigames.lustdollplus' to create a backup.ab file, then use 'java -jar abp.jar unpack backup.ab backup.tar' to create a regular tar-ball from the backup. Inside the tar, change the 'indivi.indivigames.lustdollplus' folder to 'your.new.package.name', then 'java -jar abp.jar pack backup.tar newBackup.ab' to turn the tar-ball back to AndroidBackup and lastly 'adb restore newBackup.ab'.
This all should also be doable in the Termux app on Android if one doesn't have access to a PC.
And you may not even have to change the package name. Do a backup, uninstall orig app, install modded app, restore backup without changing it, done.
Edit: can backup and restore using Termux
Install this, enable wireless debugging, connect ADB to localhost and backup-restore as above
Currently, LDE has the same package name as LDP, so you don't need to rename the folder. But yes, theoretically, once you uninstall LDP, install LDE, and restore the backup, your saves will transfer. If that doesn't work, no worries, just install LDP again and restore your backup as if nothing happened.
And let me know if it works. If it does, I might create a script to do the whole bkp-uninst-inst-rest thing.
I just tried and sadly it doesn't work, when it restores the data it doesn't go to LDE, but it does go back to LDP so I was able to keep my save. I feel like it's so close but I don't know what to do, I even checked the package name of LDE just to check they were the same and they are so that not the reason why it doesn't work. If you come up with anything else I can do to try and get it to work let me know I've had a lot of fun trying to get this to work :3
I got something.
The saves are in, they are visible, but can't be loaded. That is progress if nothing else.
Did it in an emulator without root. If you want to test it yourself, untar the backup.tar. In there you'll find an 'r' directory, upload it's contents as seen on screenshot (tar -> push -> cat-pipe-(run-as dd) -> run-as untar) and from the 'sp' directory upload that one file to 'shared_prefs', also in the run-as jail.
I'll see what I can do about the whole not loading thing.
Or I guess you could upload the backup.tar, untar it into some temporary dir and cp the files from the temp dir to their correct place. That should work too.