Facts from Robert K. Wright, "The Continental Army,"1989, Center of Military History, United States Army (the official Army account of the Revolution):
- Congress met on May 10 "resume its coordination of the thirteen colonies' efforts...It face the fact that four colonies were already in a state of war". (p. 21)
- On May 16, Richard Henry Lee made a motion that Congress form an army. (p. 22)
- By May 18, Congress head learned that Fort Ticonderoga had been captured by a force headed by Ethan Allan and Benedict Arnold. (p. 22)
- On May 31, Congress received Arnold's report that British forces were massing in Quebec. "Congress asked Connecticut to send troops." (p. 23)
- On June 14, Congress approved an American Army by authorizing the enlistment of ten companies of riflemen. They also "accepted responsibility for the existing New England troops." (p. 23)
- "The 'expert riflemen' authorized on 14 June were the first units raised directly as Continentals." (p. 24)
- George Washington was chosen as commander on June 15. (p. 25)
- Officers were appointed to various positions in the new army during June and July. (pp. 25-40)
- "the irregulars who had taken the fort under the leadership of Ethan Allen of the Green Mountain Boys and Benedict Arnold, a Connecticut volunteer acting under a Massachusetts commission, quickly melted away." (p. 40)
- "On 20 July, Congress formalized [Philip] Schuyler's territorial department as one of the basic command elements of the Continental Army...Schuyler's little army in the New York Department, contained the 4th Connecticut Regiment..." (p. 41)
- "The Continental Congress authorized the formation of a special unit in Schuyler's army as a reward for Ethan Allen's role in the seizure of Ticonderoga...They were formed into a regiment...[They] elected Seth Warner...to the command." (p. 42)
- "Schuyler... launched an invasion of Canada on 31 August." (p. 42) [More details about his force structure are given on p. 41.]
- "Washington launched a second invasion directly from Boston...On 11 September he gave Benedict Arnold...command of a special force of 1,100 men drawn from the main army. Three rifle companies (Daniel Morgan's from Virginia and Matthew Smith's and William Hendricks' from the Pennsylvania Rifle Regiments and two provisional fire-company infantry battalions of New Englanders..." (p. 42)
- "A wounded Arnold, with only a handful of men, continued to blockade the city [Quebec] as 1776 began." (p. 43)
- In early 1776, both Schuyler and Washington (acting with Congress reorganized the New York Department, separating the Canadian force and reinforcing it. (pp. 56-65)
That is the timeline as given in the Army's official history. The men that you have listed enlisted after Ticonderoga and were all discharged before Arnold's campaign on Quebec began. Possibly they served in the siege of Boston, but the march to Quebec did not start until September.
As for the name of Arnold's "regiment" during the march... It would appear that it did not have a name. If it was called a "regiment," it was certainly an oddly formed one, lacking a staff, and consisting of "three rifle companies and two provisional fire-company infantry battalions." Probably it was called simply "Arnold's men".
So, at this point, the premise of the question appears to be incorrect.
Dealing with these militia units is always tricky. Best of luck :)
