Migrate a flat /16 network to routed VLANs without a big-bang outage

A head office has about 1,500 hosts in one flat VLAN 1, 10.0.0.0/16, across 3 floors and 10 closets. The gateway is an old layer 3 switch, OLDCORE, with interface Vlan1 at 10.0.0.1/16. DHCP runs on a Windows server at 10.0.0.10 with one scope. Twice last quarter a looped desk switch caused a broadcast storm that took the whole office down. A new core pair, CORE1 and CORE2, is racked. You must move to VLANs per closet and function, with routing on the new core, and the business refuses a big-bang weekend.