Hi,
My knowledge around this issue is limited but lets get started with few queries and hopefully we can get some help from experts.
Few queries/suggestions:
1) what is the Ontap version? - This question is wrt to compatibility matrix for VSC,ESXi & ONTAP. I am guessing you must have already checked that out but no harm in getting it re-checked. http://support.netapp.com/matrix
2) http 500 error is usually not specific and can occur for a number of different reasons, so it's difficult to nail it until you diagone the logs. However, there is an error you have mentioned aroud 'java' extensions.
This one : java.io.FileNotFoundException: /opt/netapp/vscserver/tmp/jetty-0.0.0.0-8143-nvpf.war-_-any-9825894675574059877.dir/webapp/vsc.zip (No such file or directory)
Looks like it's complaining about file not found (jetty-0.0.0.0-8143-nvpf.war)?
vCenter will reach out to the VSC server and pull across a "webclient_deployment_bundle". UI extensions from this bundle are copied to directories on the vCenter server. Probably it is unable to download the bundle usign vsc address, and therefore filenotfound error.
This KB talks about 'UI extensions unable to download:
https://kb.netapp.com/app/answers/answer_view/a_id/1005302
3) Which was the previous version that was working ? so, is it 9.7 which broke it or is the upgrade to 6.7U3 ?
4) (Not likely the case but no harm in suggesting) A certificate is required for communication between vCenter, ESXi hosts and the VASA Provider of a storage array, this certificate is setup when you register a VASA Provider in vCenter Server. However, as I am reading on the google, there is a statement : By default, 6.7 U3 does not allow self-signed certificates by Storage VASA provider. So, is it a self-signed ones?
https://kb.vmware.com/s/article/74756
Thanks!