I think brown sugar goes through the stages (hard ball, hard crack, etc.) at different temps than white sugar, so I’m not sure what the correct temp would be for the butercream syrup. If you are unable to find out, you might consider making the buttercream with white sugar and adding molasses as a flavoring agent to the finished buttercream. Since most brown sugars are made by adding back molasses to white sugar, the flavor would be spot on, and the molasses would not risk any flavor alteration from the heat.
If you are worried about the buttercream being too sweet with addition of molasses, you can deduct some (but not all, to be safer from overbeating) sugar from the amount added to the soft peak whites in the silk meringue and mousseline recipes.
Please report back on your experiment!