If I want CloudFormation stack status updates to show up in a continuous delivery system in as close to real time as
possible, how should I achieve this?

A.
Use a long-poll on the Resources object in your CloudFormation stack and display those state changes in the UI for the system.

B.
Use a long-poll on the ListStacksAPI call for your CloudFormation stack and display those state changes in the
UI for the system.

C.
Subscribe your continuous delivery system to an SNS topic that you also tell your CloudFormation stack to publish events into.

D.
Subscribe your continuous delivery system to an SQS queue that you also tell your CloudFormation stack to publish events into.

Explanation:
Use NotificationARNs.member.N when making a CreateStack call to push stack events into SNS in nearly real-time.
http://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/using-cfn-updating-stacks-monitor-stack.html