Building on my prior comments/findings, this KB suggests an option of allocating a SAN volume that can be shared by multiple hosts for writing core dumps:VMware KB: Host not configured with core dump server
I also noticed in the notes of the same KB : "The slot size and VMkcore partition size are not synonymous." Any information available to help understand the differences between the slot size and the diagnostic partition size?
Either way, seems like a possible solution would be to allocate a new SAN volume and create a shared diagnostic partition on it. But I've yet to determine if that's a supported option with Host Profiles and Auto Deploy...