Just for clarity though, I'd like to ask how many more deleted posts would put me in danger of being banned?
There is no way to exactly give you an answer on this. For example, we could have two situations:
1) A section moderator / a moderator without banning privileges deleted your post(s): It is up to them whether they want to report you to someone who can ban users or not. If they do, then it is up to the person handing out the bans whether they want to ban you or not.
2) A moderator / admin with banning privileges has deleted your post(s): Now it is directly up to them whether they will ban you or not.
Generally, in the case of *seemingly genuine* person who does not participate in signature campaigns a warning is usually handed out first.