We experienced the same issue when first deploying LTSB. In your answer file you need to change copyprofile=true to copyprofile=false. That will resolve the issue. Haven't tested with 1607 so I'm not sure if it's still the same but that fixed it for us. Microsoft hasn't been very helpful about it either.
We worked with Microsoft a year ago on this issue. (We lucked out and got a pretty good MS support rep. It still took about a month to find a solution.) The problem is patched in one early cumulative updates. However getting it installed in audit mode is problematic. If you don't need or care to have items set in the profile then JForman's answer is the simplest way to go.
If like us, you want to have wallpaper and the start menu customized then it is a bit of a work out to get it done. The cleanest way is to do a fresh install. With this one do not go into audit mode. Choose to create a local login. Once the install is done, apply the current cumulative patch and any other OS patches. After the image is patched, run sysprep and put the image into audit mode. With it in audit mode and logged in as Administrator. Remove the user account you create in the initial install. Remember to both delete the user profile and the account. (don't ask me why I know this... ) You'll need to remove the "Desktop" link from the Quick Access/Jump List. There is still a bug with it pointing to the Administrator's desktop folder when the profile is copied. Make any customizations and then save the image. Because of the oddity of this workaround we haven't applied patches to our base LTSB image since we built the "fixed" one. Rather we rely on LANDESK security scan to update it.
After our work on LTSB our upper management choose to deploy Win 10 Education Edition. In building that image using the 1511 release we found that this issue was fixed in the install media. We haven't looked a newer releases of LTSB. We have just used our 17Dec15 build of LTSB for the areas that windows store apps are problematic.
Thanks for the information. I'll give this a try and report back.