The problem is that on a particular host box HKLM\SOFTWARE\Policies\Google\Chrome /v RestoreOnStartup is set to 0x04 which prevents restoration of previously open windows/tabs and that makes ChromePortable completely useless.
I tend to have like a dozen windows 5-6 tabs each and the very reason for taking the latest ChromePortable was to avoid that policy force fed to that box for the locally installed Chrome.
0x04 is "Open a specific page or set of pages" in On startup settings
0x01 is "Continue where you left off" == restore tabs and windows
Since you are already able to virtualize password(s) == intercept registry reads for particular paths can you do the same for HKLM\SOFTWARE\Policies\Google\Chrome /v RestoreOnStartup
The value(s) can be in already present GoogleChromePortable.ini or a new .ini
This is not possible without admin rights. I'd suggest using Firefox Portable.
Sometimes, the impossible can become possible, if you're awesome!
There doesn't seem to be a way to attach a screenshot here and it will be hard to grasp the Firefox problem without seeing it. The box is under a crazy VPN kept by Zscaler which messes with SSL (called SSL "packet inspection" or snooping) and plants it's own versions of de-facto fake certificates - the data in them is copied from originals but signatures are different. Zscaler was injected as "root authority" but your portable Firefox either doesn't see that at all or get;s confused by something else and refuses HTTPS connection to google.com and support.mozilla.org.
It recognizes Zcaler as: Zscaler Intermediate Root CA (zscaler.net) (t)
Error code: MOZILLA_PKIX_ERROR_MITM_DETECTED
And the the text after that states directly that Firefox refuses to do exactly what Zscaler wants it to do:
But, when I install Firefox (== definitely not portable) then it doesn't have any of these problems at all. => you'd need to convince/force Firefox under your portable setup to drop the paranoia and play ball with the host - plain install apparently does that.
Portable Chrome doesn't have any problems in that regard either