I'd just use my press and stick the necks over a pocket platen and press them that way. way easier to work with that the speedball system (I had one in the past and with no control of off contact I ruined a lot of stuff with bleed.)
Back to the topic though it shouldn't matter if the shirt started tagless, tearout, or tagged because a pair of scissors and some practice and any shirt can be tagless. In some cases an original tag might be beneficial too... such as in the case where a client wants AA shirts.
Also anyone consider other placements like bottom edge or inside a sleeve? Might prove to be an interesting discovery. Sleeves might prove useful for sizing when going through shirts on a rack too... just flip the sleeve inside out instead of having to pull shirts apart and look.