Class E is a hodgepodge airspace.
It looks like that, yes. Still: there's none here in BE but there's plenty of it in Germany, where I often fly, yet I never hear of any issues there? Perhaps they're better at hushing up...
the local IFR frequency is never published
What is an IFR frequency? I think a lot of the UK difficulties are due to the lack of a one to one correspondence between any 3-D position and a service/frequency. All over the continent, if one is at coordinates lat x / lon y / elevation z, there is one and only one service to talk to, and one frequency for all that are within their area. No question of "IFR frequencies", thus. I think the UK needlessly complicates matters, thereby increasing danger, by refusing this simple arrangement, leaving pilots the choice of a service to tune into.