What device allows me to recover a hot wire from two travellers coming from a 3-way switch?
This can be done with a relay. Some people would delight in a technical solution, while others would not want a non-standard lashup in their house. 

Here is one way, using a mains-voltage SPDT relay that is a common industrial catalog item. 



The activating coil is connected between one of the travelers and the neutral. The normally-open terminal is connected to that same traveler, while the normally-closed terminal is connected to the other traveler. The always-hot may then be drawn from the relay common terminal. 

Unfortunately this kind of relay wastes a small amount of power (the holding current) when one of the travelers is hot. 

Added in response to comments: A bistable relay does not require a holding current. These are harder to find, and probably will not fit into a residential junction box. If you can find one, you will probably also find instructions for wiring it for your application. 

But just in case you find one at a garage sale and the instructions are missing, here is a way to use a bistable DPDT to do what you want.