Short version
Is there a way to force a specific banner to show so I can take a screenshot? I know I can Photoshop it etc, but that's not really nice.
The whole thing
In name of an intermediary firm I regularly place banners for their clients on my site via DFP (my account). They always request a screenshot of the site displaying the clients' banner to pass on to them showing that I've started the campaign.
Unfortunately sometimes the frequency is so low that even "As fast as possible" takes a ton of pageviews before the banner shows up (which is also not really nice towards the other advertisers).
You can check documentation for Preview a creative
In short:
You need to open creative, click Preview tab, click on site and put url of the page on your site where you expect to see your creative
Update
Looks like problem related to way you are opening creative. I have reproduced this behaviour.