Hi Daniel,
I must admit the A310 panel is one of my favorites too... but not the most intuitive to fly, that's for sure. and the instructions are... instructive, but they mostly say WHAT commands you got not HOW to use them.
Besides the Nav/Vor/Ils knob (which tricked me too), there are a few other particular features you should be aware of:
- There are some functions on the AP (and it may be exactly the HDG & LAND) that are incompatible, but switching one ON does NOT automatically switch the other one OFF. So check which other AP functions are ON while you attempt the ILS approach.
- Most important, NEVER have both ALT and LAND disabled at the same time with the autothrottle engaged, or you are guaranteed to be unpleasantly surprised with the results
Also, though this is not a panel issue, it was most fatal for me with this plane, the AP won't be able to hold the glideslope if you are too heavy. Which is bad, unless you want to know what lies under the runway asphalt

.
Trial and error worked for me. However, the "ILS mode on the autopilot shutting off" does not sound familiar to me. What exactly do you mean by "when it should take over from the hdg function"?
Hope this helps
Andrei