Sure safety tools are tools, however the X card in particular is a very bad one for live play. Your system sounds like the best implication of the X card that i have heard, the verbal form is what I am against. Where people gotta raise their hand or verbally say no, or there is someway for people to tell it was Gary who played the X card. As someone who is disabled I hate having to be singled out because I am uncomfortable, there have been cases where speaking out about my uncomfortably has been more uncomfortable, saying that I'm sure the people I was playing with wouldn't have judged me or made shifty eyes at me but the irrational fear that they would kept me from expressing that i wanted what was happening to stop.
The other problem with the X card is that while I imagine you and other will uses this along side other tools and talking to players etc, the wider implementation of the rule is just to slap a band aid over the problem and never address underlining issues or themes with their players. I feel there are better way we can design these tools, and even better tools out there in the world that already are a thing other than the X card. Also some tools designed by marginalised people would be excellent.