The old version kept crashing my new Galaxy S3 too. However, I managed to get it running for long enough that I was able to do as previously instructed and: install, reset, and then change the path (in my case to /mnt/extSdCard) before logging in. I then saved a few songs onto the phone to confirm that they were being saved to the external SD card instead of the phone itself.
Once confirmed, I went to Google Play and upgraded to the new version (WITHOUT UNINSTALLING THE OLD VERSION or logging out, etc.). None of the settings were changed, and the new version now saves them to the same place as instructed by the old version - the external SD card.
4. install the application (make sure you have "install from unknow sources" enabled on your device)
5a start the application, and then log off in case you get logged on automatically.
5b from the login screen, click on your phones menu button, press "reset spotify" and press ok.
6a still at the login screen, press the menu button again and select "select SD Location"
6b at this point it will suggest "/mnt/sdcard" - this IS NOT your external SD card. This is your phone's internal memory card. You need to change it to "/mnt/extSdCard" NOTE: this is from my Galaxy S3, and may vary from phone to phone
7 once this has been changed, test it - note both the phone's memory status and the external SD card's, and see which decreses after saving a few songs
8 If it is now saving to the external SD card, visit Google Play and upgrade to the new version of Spotify (WITHOUT UNINSTALLING THE OLD VERSION or changing any settings)
If this doesn't work for you, then I don't know what will - apologies. Hopefully you were simply not doing part 6b correctly...