As above really, a lot of the advice here (including mine) is only worth what you paid for it.
None of the examples you've given are particularly realistic to real life, and the same goes with any textbook trying to explain it, you just need to get out and understand what the instrument is telling you, and use the RMI effectively to help you build a mental picture.
A realistic example is taking off on runway 27, then trying to establish on a specific radial. Any radial, doesn't matter, lets just say 300. All I'm going to do is steer initially in the rough direction, then taking the wind into account I'll stick my heading 20-30 degrees to the relevant side of the radial in order to intercept it, lets say 320. As soon as I then see the VOR needle twitch into life I'm going to steer onto a wind corrected heading to track and hold that radial.
When you are very close to the beacon, you can use a small intercept angle, say 20-30 degrees, but you will need to be quite quick with a lead in turn to establish on the radial, otherwise you shoot through the other side and have to turn back onto it.
When you are far away from the beacon, say 30 miles or more, you may end up using a 60 degree, or in some cases 80-90 degree intercept to get onto the radial, but as you're so far away the needle is less sensitive, so you will wait until the VOR needle is almost in the middle before you start turning to track and hold it.
The whole "I'm on this radial and need to be on that radial" type question doesn't happen in real life line flying, it's only IR instructors trying to prove a point who will throw it at you, and while it does have some training value, it's not the only focus, and you just need to be aware of where the aircraft is in relation the beacon, and visualise how to establish on the radial you desire.