For vcxsrv there is a .xlaunch file with xml-config that may enable clipboard (launches after installation). Mine is config.xlaunch:
<?xml version="1.0" encoding="UTF-8"?>
<XLaunch WindowMode="MultiWindow" ClientMode="NoClient" LocalClient="False" Display="0" LocalProgram="xcalc" RemoteProgram="xterm" RemotePassword="" PrivateKey="" RemoteHost="" RemoteUser="" XDMCPHost="" XDMCPBroadcast="False" XDMCPIndirect="False" Clipboard="True" ClipboardPrimary="True" ExtraParams="" Wgl="True" DisableAC="False" XDMCPTerminate="False"/>
X servers on Windows are often a bigger cut/paste barrier than tmux. As you mention, vcxsrv seems to work better than other choices. Note there are some cut/paste/clipboard options you have to set.