judge could easily decide that you putting tape on the object will chnage the object.
Isn't that stretching things quite a bit as long as the tape can be removed.
You are always at the mercy of the event supervisor at your tournament. It's impossible to predict how they might interpret any given paragraph without asking them. I have observed cases where an event supervisor changed their interpretation and penalized a team for something they had previously said was OK.
If you are limited by any possible interpretation a judge may make, it could be very difficult to do anything. For the Mystery Material to be "Significantly incorporated" into the device almost dictates that some method of attachment be allowed. The only requirement is that the Mystery material remain "undamaged". This, of course is open to interpretations is any other language in the rules.
Again: There is no way of knowing how it will be interpreted without asking the event supervisor at your tournament.