My thought here is that the moment you use that one cue solely as your breaker it becomes a specialty cue. Whether from your case or off the wall, if you use that cue to ONLY break it becomes a speciality cue.
In the sketchy bar when you played with your breaker, because you didn't use that cue to only break but also as your player it was not a specialty cue and was a regular shooting cue.
If I use my factory stock BK 2 to play an entire match with, then for that match it was a regular shooting cue because that's how I used it - as a regular shooting cue. The player in the next match barrows it to break with and uses it only as a breaker. In that match it is a specialty cue. In the following match the next player barrows it and uses it to break and completes his first inning with the BK 2 but switches in the second inning to a different cue. Once again it ceases to be a specialty cue because it was used, albeit briefly, as a regular shooter.
Whether it's an Orange Crusher, or a BK 2, or a Schon CX86, or a $10,000 Southwest, it's in how you as the player uses it during a match that makes it a specialty cue or a regular shooting cue. What the manufacturer might call it means absolutely nothing, it all in how you, the player, choose to use it.
The rule/definition regarding a breaking cue refers to "a cue designed for breaking". The rule makes no reference to who may have designed it, the specific design, or why you feel it's better for breaking. It gives no criteria for a break cue other than a cue designed for breaking. When you as the player use a cue only to break with and not to shoot "regular shots" with, you are, in effect, saying, "This cue in it's unique make up and design and as far as I'm concerned, is designed for breaking. Even if only for me and even if only for this match, this cue is designed for breaking.
By using a cue solely as a break cue you are making a declaration that this is your break cue and that's what it's for, even if only for that game or match. You may have purchased or acquired it as a regular shooting cue and have used as such in the past, but the moment you execute a break shot and you switch to your shooter immediately after, you've declared that the cue you broke the rack with, it's unique design, is solely your breaker and for that match or game it is by declaration and thereby definition a specialty cue.