Unfortunately, the single connector for everything was a no-goer, but I did get everything down to two connections. The power connector is the first, the second is a USB connection to a Belkin USB 3.0 hub which is our standard laptop dock. Plugged into that USB hub are 2x Plugable USB 3.0 to DisplayPort adapters. These aren’t the cheapest, but they are rated for resolutions up to 4K, which covers the ultrawide’s 3440×1440, and they won’t need replacing if the bosses decide that they want to upgrade to 4K.
The solution isn’t as neat as I would have liked, as it leaves only one free USB port on the Belkin hub. Plus, the USB connection means the monitors are powered by the XPS 15’s integrated CPU graphics rather than the discrete Nvidia card, but the result is fine for office work and the odd video.
Only one driver was required for the Belkin dock, and after two weeks they have been been rock solid. Dell, take note.
Update 02/03/2017: this wasn’t the end of it. More here.