Hello Ken,
if the two core C6500 switches are in VTP transparent mode they keep their vlan database local.
if you change the vtp domain name to that of the C45xy the revision number is reset to zero and all the vlan database is lost overwritten by the current vlan database in the serve of the C45xy domain !
I think you have different choices:
or you kept the two C6500 in a different VTP domain in transparent mode and you configure the the trunk ports as nonegotiate (and as trunk port no negotiation can occur at VTP domain boundary).
Or you have to define all the vlans used in the core switches also on the C4510 VTP server. (notice all vlans not only those that you want to propagate to C45xy)
If you do so you can then move the C6500 to the VTP domain make them servers and they will learn all the vlan database from the server.
You need to schedule a maintanance time window and the suggestion is to migrate one C6500 core switch, verify everything is well (vlans, SVIs and so on) and then to make changes on the second core switch.
In the short term it is easier to keep them as VTP transparent in another domain.
if you choice to do so I recommend to make VTP server the second C4510 to have redundancy.
To help protect the network deploy MD5 authentication (if you are not doing it already)
Hope to help
Giuseppe