VS Code integrated terminal: How to access suggest widget and PSReadLine MenuComplete via Ctrl+Space?

In VS Code’s integrated terminal, Ctrl+Space by default triggers the terminal’s suggest widget, but this doesn’t show anything after e. g. <command> - or [<type>]:: although the PowerShell extension is running.
You could assign a different shortcut to PSReadLine’s MenuComplete via Set-PSReadLineKeyHandler, but for me, this would be a poor option, considering how used I am to Ctrl+Space, as well as using a different shortcut for the terminal’s suggestions.
When I saw the conditional expression terminalSuggestWidgetVisible used in the default VS Code keybindings for Ctrl+Space and the command workbench.action.terminal.sendSequence, I thought it would be nice (and should be possible) to have Ctrl+Space trigger PSReadLine’s MenuComplete when you hit it one more time after VS Code’s suggest widget has been shown, so you can use the same shortcut for both. How can that be accomplished?