And is there some sort of unicom across this uncontrolled expanse?
Generally, no. There is no requirement to talk to anyone when you're in uncontrolled airspace. In fact, as long as you stay in uncontrolled airspace there's no requirement to carry a radio on board even.
Having said that, on a volunteer basis you can use various services:
- Generally each country has an INFO frequency or two. This is typically not radar based, but it will give you flight information such as the local QNH (air pressure), weather advisories and such, and may help you to open/close a flight plan, will keep an eye on you when you're flying over water and so forth. They normally do not provide traffic information though.
- The UK has a well defined system of "ATSOCAS" (Air Traffic Services Outside Controlled Airspace) services. There are various levels (Basic, Traffic, ...) which will help you navigate through busy airspace. Some of these levels are based on radar and will give you traffic information.
- In the UK in particular there's also a system of "listening squawks", where you monitor the frequency of a nearby controlled airport, and squawk a certain code to indicate so. You don't initate comms with that controlling agency, but if they need you they can talk to you.
But to answer your question, no, it is very rare to have a "unicom" frequency where traffic just talks to each other in the "open FIR". This is typically only found at fully uncontrolled fields, to coordinate landings and departures between aircraft.
The other thing to realise is that if you're 2000 feet up in the air your radio comms will cover a vast expanse. I haven't done the sums but you can probably reach aircraft at 2000 feet that are 100+ miles away. If within such an area everybody would start to self-announce its position and intentions, the frequency would become totally congested, nobody would be able to keep track of other relevant aircraft and the net result would be that the frequency would be useless anyway.
There are some places that do have such a unicom frequency, but these are typically well-defined VFR routes that lie between congested controlled airspace - the Hudson corridor comes to mind. Such places typically do come with their own set of instructions on how to fly them, and how/where to self-announce.