Thanks! That information really cleared things up for me as to what these other partitions are used for. I suppose given we are booting via Auto Deploy, stateless caching is creating the partitions to boot from disk so the behavior can be similar to a stateful install.
One thing I found interesting ... partitions #1, 5, 6, 7 and 8 are all 33 sectors apart. However, partitions #8, 2, and 3 all line up next to each other (i.e. 1 sector apart.)
Assuming a 512B size per sector, the 33 sectors creates a 16.5K "gap" between each of those first 5 partitions. Wonder why...
I speculate, since I'm using stateless caching via Auto Deploy, I could recreate the partition table on the local disk to include a resized diagnostic partition #7 of 300 MB to match the slot size setting, but I suspect this might be unsupported. Looking more closely at the KB2012362 I linked in my original post: "The default partitioning scheme and VMkernel core partition for ESXi cannot be modified to accommodate for larger core dumps. To be able to record core dumps that are larger than the default VMkernel core partition, an alternative location must be defined."
Sounds like what I could also possibly do is create a second, 300 MB diagnostic partition on local disk that exists in addition to the default created 110 MB partition #7? I may open a support ticket with VMware to find out. Doing this might mean when a PSOD occurs, you see indications that 2 core dump slots exist vs. the typical "using slot 1 of 1..."