You cannot do this. Check out the link here. Windows 7 Professional to Windows 7 Ultimate is possible but not Professional to Enterprise!
Reason? Licensing is the key here. Enterprise is the volume license and comes with a different set of bits for that licensing model. Whereas, 7Pro and 7Ultimate are built around the same licensing and come with a different set of bits. So the cool thing is you have the 7Enterprise license, the not so cool thing is there is no conversion or easy upgrade. You'll have to either reinstall 7Enterprise and all the apps or start over with your 7Enteprise image. If you're worried about losing work, I would back users backup to a central share wipe clean and start with 7Enterprise image or install then restore your user files. If you're worried about settings you can run USMT or Windows Easy Transfer to help you getting files and settings then restore on your fresh 7Enterprise image.
If it's only a small number of computers and you're needing this fast, the quick way is to run ultimate in it's place. Featurewise, 7Enterprise and 7Ultimate are just about identical. So you'll not lose anything by going to it. The cost is minimal if the number of computers is small.
Even so, there's something else to consider, you're not addressing the issue as much as working around the issue. 7professional should be able to work in a domain environment with GPOs. If you have the time, I would suggest you do a little research and testing of what is happening here. You may find it's a just a missing patch or update and that might solve your GPO problem.