Propagation maps are looking bleak between Europe and North America. That said, actual results have been good between about 2200 and 0300+ (I'm not sure about the end time because I haven't seen loggings past this time).
I used the VOA propagation models at http://www.voacap.com/. The images depicted here all come from that site. Feel free to go to the site and check propagation for your region. For transmission power and mode, I used 100 watts of SSB because that seems like a pretty standard baseline for North American pirates & for at least some of the European pirates who might want to be testing specifically to reach across continents.
For the first image, I used Harrisburg, PA, as the location because it's the closest one to my location and that way no one will feel like I'm giving away their location. Here is 100 watts into a dipole about 30 feet above the ground on 14.1 MHz (essentially the same for either 13900-13950 kHz or 15010-15090 kHz) at 1500 UTC.
Next is 2000 UTC using the same specs:
Turning to Europe on 14.1 MHz, I've chosen The Netherlands for my target country. Here's that frequency with the same 100 watts in SSB at 1400 UTC: