The Stoßtrupp Adolf Hitler did not wear a cuff title, as cuff titles of any kind had not yet made their appearance in the Nazis' garb in 1923. (Neither had collar patches and shoulder boards, for that matter.)
Later, the Stoßtrupp was considered not just the forerunner of the LSSAH, but of the SS as such. In 1939, Gunter d'Alquen wrote:
"Die SS entstand in ganz früher Zeit der nationalsozialistischen Bewegung, im Jahre 1923. Sie wurde dann später als "Stoßtrupp Hitler" am 9. November 1923 automatisch mit der gesamten Bewegung verboten und aufgelöst."
["The SS was formed in the very early period of the National Socialist Movement, in the year of 1923. As the "Stoßtrupp Hitler", it was later automatically prohibited and disbanded along with the entire movement on 9 November 1923".]
(From: Die SS - Geschichte, Aufgabe und Organisation der Schutzstaffeln der NSDAP)
The Stabswache Berlin/Sonderkommando Berlin, Sonderkommando Jüterbog and Sonderkommando Zossen only existed within an overall timeframe of less than a half year's length between mid-March to early September 1933 (having been formed at various dates during this period) and - unsurprisingly, given their transitional nature and short existence - did not have distinctive unit cuff titles. They would have worn cuff titles following the A-SS' system (with company numbers etc.). Perhaps our member d'alquen has more precise data on this matter.
These individual units evolved into what was initially known as the Adolf-Hitler-Standarte and soon became the Leibstandarte. The first distinctive cuff title worn by Hitler's armed bodyguard formation was the short-lived "Adolf Hitler" one in Gothic letters which after a year or so was replaced by the Sütterlin pattern. Initially, other SS units/institutions also utilized cuff titles in Sütterlin script, but this was eventually reserved for the Leibstandarte only as one of a number of distinctive features in its accoutrements.
The 5 May 1934 order on the insignia worn by the Politische Bereitschaften mentioned by you did not introduce the "Adolf Hitler" cuff title, but merely confirmed it:
"Die Leibstandarte S.S. Adolf Hitler behält ihre eingeführten Abzeichen (Ärmelstreifen mit der Aufschrift Adolf Hitler, Kragenspiegel: rechter Krangenspiegel bestickt mit der S.S.-Rune)."
["The Leibstandarte S.S. Adolf Hitler retains its established insignia (sleeve band with the inscription Adolf Hitler, collar patch: right collar patch embroidered with the S.S. runes)."]
(From the Mitteilungsblatt der RZM of 23 June 1934)
The "Stoßtrupp Adolf Hitler 1923" cuff title was an honorarium worn on the right lower sleeve of political uniforms (not just SS, but also SA, PL etc.) by former members of the original Stoßtrupp. The circle of wearers was very small (some 50 or so men, if memory serves) and included such well-known "old fighters" as Julius Schaub, Emil Maurice, Karl Fiehler, Ulrich Graf etc.:
"Ärmelstreifen: Stoßtrupp Adolf Hitler 1923
tragen auf Anordnung des Führers ehemalige Angehörige des Stoßtrupps Adolf Hitler 1923 beim Dienstrock und Uniformmantel am oberen Ende des rechten Ärmelaufschlages, bei der Dienstbluse am rechten Ärmel, und zwar 1 1/2 Handbreite von Unterkante Ärmel.
Ausführung: 25 mm breit, Ripsstreifen aus Aluminium, Schrift in Schwarz."
["Sleeve band: Stoßtrupp Adolf Hitler 1923
is worn, on the Führer's order, by former members of the Stoßtrupp Adolf Hitler 1923 on the upper edge of the right sleeve turn-up of the service tunic and uniform greatcoat and on the right sleeve of the service blouse [i.e. the brownshirt] namely 1 1/2 hand's width from the lower edge of the sleeve.
Design: 25 mm wide, rep band made of aluminum, lettering in black."]
(From the 1937 edition of the Organisationsbuch der NSDAP)