AWS has something built in called cloudwatch alarms that can handle the basics.
You could also use a Lambda Function. Give it access to the ASG, and then have cloudwatch configured so once the min amount of traffic starts coming in it sends an Event to the Lambda.
And once ...
Have you been in this scenario before?
Yes. Pretty standard scenario in my experience.
How did you address and overcome these obstacles?
In very small steps.
How long did it take to implement? (as a rough idea)
Very long; in one rather large extreme case: over 10 years, and still ongoing.
How would you prioritize the tasks listed above?
I'm not very familiar with Jenkins on Windows, but I imagine your issue lies in the fact installing Jenkins on drives other than C:\ are more difficult to deal with. Since Jenkins is not running, you'll have to configure config.xml by hand.
Here's a post on stackoverflow.com that may help you. As they state, you'll probably need to find the Workspace Root ...