Why can't I move an iTunes gift card?

Question

I just got our SeniorNet Computer Learning Center into Apple computers and tablets two years ago (Dec 2011) and I'm beginning to wish I hadn't. Here's the latest "policy" problem with Apple I've encountered.  We have 10 Apple computers and 14 Apple tablets (iPads) and I've created unique Apple IDs for each device. When I upgraded the software on the Apple computers I had to assign my PERSONAL credit card to the account long enough to order the Mountain Lion upgrade and then I immediately removed my credit card from the account. I didn't like doing it because all of our students know the Apple ID and password for each computer so there was an exposure but I lived with it. However, it would be MUCH better (and SAFER for me), if I could order the upgrades for the desired Apple IDs, using my personal Apple ID account. I keep hoping Apple will hire some smarter people that might see the flaw in their current policy and change it.
Now, onto the latest policy problem. As part of teaching the iPads, I wanted to have a song on each iPad, purchased from the iTunes store. You already know my concern with assigning my PERSONAL credit card to an Apple ID account created for our computers so I really didn't want to follow that procedure in order to purchase a song for each iPad. My solution was to buy a $25 iTunes gift card. I could then apply the gift card to the first iPad Apple ID, purchase the desired song, then remove the gift card from that Apple ID and apple the gift card to the next Apple ID. That way, our maximum monetary exposure is whatever the balance is on the gift card rather than my available credit on my PERSONAL credit card. Sounded like a much safer plan than having to enter my PERSONAL credit card information on each Apple ID for all of our iPads.
Now, we encounter the latest DUMB Apple "policy".  It was really easy to redeem the Apple gift card on the first Apple ID. I scratched off the label to reveal the code, entered it into iTunes, and was able to purchase a song for that Apple ID. Now, all I had to do was to remove that code from that Apple ID and move it to our other Apple IDs in order to purchase the remaining songs. The iTunes gift card balance would follow it, just like gift cards you purchase anywhere else.
I went into the account for the first iPad in order to remove the gift card but was unable to find out how to do it. I went into Apple Support and sent an email, asking how I could remove the iTunes gift card from the current Apple ID and move it to the next Apple ID. I just received a reply back this morning from Aaron: The BAD NEWS, currently, once you redeem an iTunes gift card on an Apple ID, you can't remove it from that Apple ID!!!  I'm now stuck with an iTunes gift card with a balance of something over $23 and I'm unable to use it to purchase the other songs for each of our other iPads! I have no reason to purchase anything else from iTunes for that Apple ID so our SeniorNet Computer Learning Center is OUT the remaining balance on the iTunes gift card!
Apple needs to CHANGE this policy, IMMEDIATELY!!!

Answer 1

It says, cannot complete transaction, contact iTunes support.  When I contact iTunes support it leads nowhere specific.