When running GoogleChromePortable.exe, stderrerror is not redirected from the chrome.exe process (some information is presented this way for devtools etc).
Is it possible to make the portable .exe redirect stderror from the child chrome.exe process somehow?
I don't think it can be redirected up the process hierarchy. If you need it, you'll have to launch chrome.exe directly. You can use the --user-data-dir= command line switch to redirect the settings to use the ones in your GoogleChromePortable install, but it won't be fully portable.
Sometimes, the impossible can become possible, if you're awesome!