Well I couldn't get the Console to work with my Apache ProxyPass Server and then read about how people have used nginx successfully and after further reading found out it is basically built to be a proxy server. So long story short, here is my preferred/updated config for NGinX ProxyPass with the esXi html5 webclient with websocket support and SSL.
It is not necessary to install your ssl in the esxi host, but you can :)
Here is my page for NGinX Reverse Proxy.
But a few specifics about esxi html5 client.
First off the default folder /ui requires files below it in the web directory, this means proxypassing the /ui won't work and instead you need to proxypass the default webroot
and manually type /ui.
I put in a request to have the necessary files linked to /ui, so this may not be necessary in the future.
The only problem with proxypassing the default webroot is that if you don't type ui people can see the welcome screen. I actually moved everything from /ui into the default webroot @ /usr/lib/vmware/hostd/docroot/
[Update] I now use
rewrite ^/$ /ui permanent;
Interestingly if you screw up, or even if you don't esxi repopulated the entire web directory after reboot even the /ui folder. So this workaround requires a reboot script or it isn't persistent.
I am not sure why, it could be my configuration, but I was also unable to proxy domain.com/path to https://ip/ successfully, I instead had to create a subdomain and proxy subdomain.domain.com to https://ip/
NOTE during testing always use a trailing slash after /ui example https://subdomain.domain.com/ui/ -.... that took a while to figure out... and there was nothing wrong with my configs!
One thing I like about nginx is you can move things outside the server perameters and make them global to that configuartion file which is what I did. you can also include common configs, please read my linked page for NGinX above.
On to the configs!