Happened upon this thread, maybe this will help or maybe not. You can decide. I am currently in a debate over the existence of the Christian God, who I believe to be the one true God while all others are false (https://www.debateart.com/debates/1388/the-christian-god-does-not-exist, I'm not trying to advertise, just showing evidence that it's true). As far as I can tell, deism and theism are just terms stemming from the word "god" in Latin and Greek respectively. We have attached additional meaning to them. If you're just differentiating between them by saying Deism is belief in any god, and theism is belief in a particular god, then I believe you can argue from both. Logically, it would make sense to justify the existence of a god in general to exclude atheistic arguments, and then move on to justify the existence of a particular god to exclude arguments for any other god.
Now if you're using deism in the sense that a deity created the world and is no longer active (like setting a top in motion and then sitting back to watch it spin where it will), then you would be right that theists should not use this specific argumentation if they believe that their god is still active in the world. Based upon these definitions, I would argue strictly from a theistic perspective and vehemently oppose deistic argumentation. The overall point of this, I am using theistic arguments, with evidence, to prove the existence of a particular God. This should satisfy P2. However, the addition of the word "compelling" is subjective since you may not find it compelling but others do. If you dismiss my argumentation for my God on the basis that you do not find it compelling, then we would have to know, what would qualify as compelling evidence according to P2?