The ESXi web client interface is presenting a screen resolution issue (takes a 1024 x 768 screen and presents us with a 1024 x 767 screen - saves the top row of pixels for restoring the hidden banner) so we tried moving to using VMware Remote Console (VMRC) plugin. In VMRC we discovered the same issue of repeating characters when using the keys() method. We discovered this can be mitigated by either disabling the "repeat key" capability in the host OS using the Windows "Ease of Use" feature, or through a VMware setting (https://kb.vmware.com/s/article/196) which increases the timeout VMware uses to register a keypress on the remote system and sending repeats of that character.
I should note that we don't see the repeat keys or have any issues doing this manually. Only when trying to interact with the VM host OS using TestComplete.