I'd go with non-adoption.
You may remember that the rules about not voting for Cancel when you don't honestly want to cancel as a means of communication in No-Messaging games **predates** that of the Hidden Draw Votes feature. The reason for this is that for some time periods of the site in some amount of players there was a cultural meme of voting "cancel" to mean "Let's eliminate the smaller players and then draw, i.e. I'm willing to draw soon, just not yet". (as others have pointed below, that could just go to Pause as well)
0) So it really isn't a unique feature to Hidden Draw Votes.
0.5) This is only against the rules and unethical in gunboat games, not sure why you're bringing up press as well.
1) I'm against adding additional features just to try to stop people from cheating in ways that are already against the rules. Having a log of votes would be more helpful to solving the problem without having these problems of non-solution and, to pull a phrase from Linus, breaking user space. Or canceled games not being deleted from the database entirely, which has also been proposed in the past. If the major sticking point is that we can't police it well enough, then we need better tools, not taking away essential features.
2) Especially because this **doesn't actually stop the rule breaking**. We have plenty of rules on the site that can be broken if someone wants to, and if they do we'll investigate and determine if it happened and if so mete out some kind of adjudication. This doesn't solve the problem, and it's a problem in a problem-space we've purposely decided not to tackle. You can still just vote cancel to communicate you want to draw soon without having to vote draw. Or pause. And with this scheme there's even less risk to mal-intended cancel votes since others can't have their cancel up without taking down their draw.
3) If someone isn't voting draw/cancel in a ruined live game for 90 minutes because they think they can exploit it to win
a) That's not against the rules here, and most likely won't be any time soon unless someone wanna propose, pass, and develop an algorithmic implementation and implement it.
b) ....this change wouldn't do anything towards that problem. Because they're not voting at all.
4) This isn't a huge problem. I run into it, as a player or as a mod, very infrequently. And like I said, we investigate it when we do, just like any other form of rule breaking.
So, in addition to this proposal not solving the problem, it opens up a plethora of hugely damaging problems, many outlined by others above.
5) There's plenty of legitimate reasons to vote both draw and cancel, as you are not trying to signal you actually want one or the other. There's no reason to break this.
6) This problem refers to gunboat games, where you can't communicate, so players can't just talk out whether a game should be cancelled or drawn and need to be able to express both solutions as palpable. Telling them to just keep toggling and help the others noticed is a non-solution.
7) Hiding the cancel feature behind modmail is a non-starter for live games. Shouldn't even require further comment; and there's no particular reason to put that on the comedy cubes if there's unanimous alive agreement like is already required.