Another strong contender for a dismounting unit could be a Mountie available to the Canadian Revolution. The Mounties were primarily a frontier police force, but they also drew heavy influence from military units and served as soldiers in several wars such as the Northwest Rebellion and Boer War.
When mounted they could function similarly to Carbine Cavalry, but with a stronger melee attack using a lance. When dismounted they would function as musket infantry. Both stances could have a bonus versus outlaw and mercenary units to reflect their role as police.
The NWMP were used to control Canada’s frontier and garrison forts such as Fort Walsh. To reflect this, they could also have the ability to construct Forts and Trading Posts.