Cannot change iCloud ID in iOS8 - Can't Sign Out without turning off Find My iPad - which needs the password for the old iCloud ID

Question

I have read the older responses to questions re how to change the iCloud account from an old ID/email address (OLD ID) - to a new ID/email address (CURRENT ID).  They all say go to Settings>iCloud - and Delete the iCloud account.  In iOS 8 - there is no Delete - but there is a Sign Out.  BUT - when I choose the Sign Out it shows a pop-up with the OLD iCloud ID - saying I must first sign IN to iCloud and enter a Password Required to turn off the Find My iPad feature.
I have tried using the password I remember as being correct for the OLD iCloud ID.  Doesn't work.
I have tried using the password for the CURRENT ID - even though the pop-up has the OLD ID displayed.  Doesn't work.
I'm out of ideas - except Reset??
Should I Reset All Settings? 

Answer 1

I finally found a work-around in another thread on this Using iPad community.  Basically, I had to first make sure that the Messages and Facetime were associated with the CURRENT/NEW ID.  (I could do this by simply erasing the OLD ID and typing in the new - in General>Messages and General>Facetime.  I then used by PC to change my Apple ID back to the OLD ID/EMAIL - but leave the new password alone. 
I then went back to Settings>iCloud - clicked on Sign Out.  When it asked me to log on -- with the OLD ID/EMAIL -- to turn off the Find My Phone - I did so using the Password that was originally used with the CURRENT/NEW ID.  This worked.  So I finally was able to close out of the iCloud account that used the OLD ID/EMAIL.
I then went back on my PC to change my Apple ID back to the CURRENT/NEW ID/EMAIL.
I then went back to the iPad Settings>iCloud - and signed on using the CURRENT/NEW ID/EMAIL.
So everything is OK now.
WHEW!!!
Not sure why this has to be so difficult.  But thanks everyone for your suggestions.