Yes it certainly could be related to the carotid blockage.
If your Dr has recommended that you have this taken care of surgically,I suggest you do so as untreated it can lead to worse problems.
Even though your heart rate
is 60-65 at rest,it tends to slow down alittle more when you sleep.
Upon rising in the mornings you are kinda "kick starting" the heart for the day and it is speeding up until it gets itself into the rythum it needs to be at for whatever mode you are getting into.