problem is that setting is used only when it runs scripts to upgrade the database and is only used in the case where the user on the connection string is not dbo, what happens is it replaces dbo. with the setting in the scripts before it runs the scripts that create the tables and stored procedures. so that setting if you change it isn't going to change the fact that the database already has that prefix in the stored procedures.

I do not have a solution for the problem if the owner prefix is not the same after you moved the database

MSSql42668 is coded into all your stored procedures that were created when the site was first installed because that was the owner prefix at the time.  If your host had let you use dbo this problem would not be happening for you now because you could use a different dbo user in the new database copy.  That is one reason why it is best to use a user that is dbo (database owner) of the database when the site is installed. 

to change it now you would have to actually edit all the procedures manually and there a very lot of them.

I think that in the beginning when the site was first installed if you had used this:

<add key="MSSQLOwnerPrefix" value=" " /> a space

instead of

<add key="MSSQLOwnerPrefix" value="[MSSql42668]." />

then it might have worked because it would have replaced dbo. with empty string instead of with MSSql42668. 

and that might have worked