I have been in contact with Elgato and all other stream deck vendors have made holding down a keyboard modifier work. Can I use BetterTouchTool to override "programmed" buttons on the Stream Deck Plus and Neo? Their current version is V7.5.1.
BTT interoperates with the Elgato Stream Deck in one of two ways, determined by the setting
"Stream Deck Operating Mode".
If you choose "Fully controlled by BetterTouchTool", then BTT takes over full control of the Stream Deck, and you can do anything you want, including overridding how/when any SD button press works. I think this should do what you describe, but I have to say that I haven't tried to do this specific thing.
The drawback to using "Fully controlled by BetterTouchTool" mode is that you will have to build your entire button/menu setup in BTT. If you already have a working setup in the Elgato software, this might take you some time. BTT is much more powerful, so you might be happy with the final result.
If you instead choose "Stream Deck Plugin" mode, then I doubt you will be able to override how the button press actions work on keyboard modifiers, but I don't use this mode, so maybe someone who does can correct me.