Just as a bit of an update, I finally got a chance to sort this.
The rods attach (well they at least do on my 2003 MkII Carens) with plastic clips that they snap into before the rod bends 90 degrees.
The upshot of that is, they will gently lever out of the clips, before being removed from the hole / socket, the end of the rod locates in - then they just slide out of the holes (once not being held by the clips).
I removed the handle from the door - my previous attempts to use epoxy to hold the crack in the plastic, wasn't robust enough to hold it when lifting the handle. So I realised I was going to have to remove the handle and drill it, then put a screw or bolt in it.
With it off the car, I drilled from both sides (my 3mm drill bit is pretty short), then superglued the crack, then put superglue on the screw before screwing it in. I put a screw in from the top of the plastic. The screw didn't go as far in as I'd liked, really, but then easily far enough to sort out the crack that had opened.
It's not that easy to drill, unless you completely disassemble it - one end is very "shiny" so until you've got a hole started, or managed to create a sufficient indent for the bit to bite, it slides around. Plus, the plastic narrows at times, with hollowed out sections, so you have to be mindful of that when drilling.
Put it all back together, and works perfectly.
Things I learnt from doing it? Keep all the screws and plastic covers in a little bag, as soon as you've taken them from the door. The black plastic triangle by the mirror gently levers off. Once all the screws are removed (2 x grey plastic ones, hinge side of the door, 1 x metal bottom rear corner, 1 x metal inside door pull, 2 x metal behind the door grab handle; also one grey blanking cap from the door pull screw, 2 x blank blanking caps from the 2 screws behind the grab handle - this was the passenger side front door), the door panel will need lifting up over the lip at the bottom of the window - in my case, no real brute force was require, just gently lifting it, then out. Then unplug the window switch harness.
After that, gently peeling back the membrane on the door, so that the silicone sealant stays on the membrane, so you can easily put it back in place afterwards. Other than the rods going to the door handle (one for the actual door latch, one running from the key switch), the door handle is attached to the door by 2 10mm nuts. If you drop one inside the door - as I did - it's not to bad to retrieve it, as you can gently peel back more of the membrane on the door to get access.
Having done it once, if I had to do it again, I suspect I could do the whole thing, start to finish, in less than 30 minutes.