As counterintuitive as it is, unchecking the Trigger a build on each check-in
checkbox should solve this issue as long as you have Quiet Period enabled for long enough that all of the checkins are included.
Essentially Trigger a build on each check-in
actually means "only include 1 checkin in each build." Disabling the option will still cause builds to be triggered by checkins, but will include all checkins (from all users) that occur before the build actually starts. TeamCity should really clarify this in their documentation or rename the option.