Combine Dual Datacenters with VRRP?

I have 2 datacenters in separate buildings, and I'd like move to a design that provides less L2 overhead, adds some resiliency, and makes it easy to transition to a better architecture over time. Unfortunately a complete redesign is out of the question, so I'm limited to working with equipment we have on-hand.

DC1 currently lives directly on building 1's semi-collapsed core, and DC2 lives in a ToR/access switch connected to building 2's distribution switch. Layer 2 server and storage vlans are stretched across the core and distribution. Routing is handled by OSPF.

My goal is to remove L2 from the core & distribution and eventually consolidate to a single DC through attrition. I've been thinking about moving each DC onto two L3 switches on each side, and connecting them with VRRP for server VLANs. There's enough fiber to cross connect them (i.e. each router connects both to the core & distribution switch) for a some additional resiliency, but I'm getting confused of how I'd handle that config or if the design is viable.

Unfortunately VSF isn't an option because it's not supported on the hardware I have available. VxLAN was another option I was thinking about, but it's also not supported on current hardware.

Let me know if you have any resources or suggestions, thanks!