Can WebBrowserComponent forward key presses to the DAW?

Running into an issue using the WebBrowserComponent as the GUI for my plugin. Whenever the part of my GUI that is a WebBrowserComponent is in focus, all key events get “swallowed” up. This means that if any controls are moved within the web browser and for instance the user presses spacebar in a DAW, the DAW’s transport doesn’t start. (It does if a non-WebBrowserComponent part of the GUI is in focus). Same idea with any DAW hotkeys that are pressed while the WebBrowser is in focus. Is there any way that this issue can be resolved in JUCE?

We have worked around the issue on Mac with a series of hacks for injecting Javascript into the web browser to get key events and then forward them onto the app using NSApp performKeyEquivalent, but have not found a similar hack to work for Windows, as it does not appear possible to send keystrokes to a window unless it is in the foreground using SendInput. (Though maybe a Windows expert can tell me if I’m wrong on that) And would be ideal to avoid hacks like this in the first place if possible.