Thanks to Dan Schorr of Northern Wars and Daniel Weßelhöft of Immota Fides on the history of the Brunswick army for their help in identifying the two regiments from Brunswick-Wolfenbüttel that entered English pay in 1694. Though the picture is not complete yet...
Leibregiment zu Fuß Rudolf August
Probably formed ca 1692, and may have been called Leibbataillon. There was a Leibgarde zu Fuß from Rudolf August, the duke of Brunswick-Wolfenbüttel, but the connection is not known. The battalion/regiment was commanded by a certain Oberstleutenant von Oberg. Probably this is Jobst Aschen von Oberg who saw service in a Brunswick regiment in Dutch pay before. After the war the regiment was most probably disbanded.
Regiment Infanterie von Hering
This regiment was raised ca 1693/94, and probably solely intended to hire out to England. Its colonel was von Hering, most likely Georg Albrecht von Hering, who had served in a regiment in Dutch pay before as well. The regiment was dissolved in 1697.