Update:
A mate has organised a camping trip for the end of the month, so I pulled my finger out today and started fixing the things I could see needed repair for rego. The aim is to get it inspected sometime later this week.
First item was a wonky wiper arm, which turned out to be a real pain. As soon as I noticed it was wobbling I groaned, because to get to the wiper arms in a Carry you have to remove the entire dashboard! Long story short it took me about an hour to get to the problem part, which was a worn out shaft housing. Basically the axle that the wiper arm bolts onto is alloy, and so is the casing.

So from years of use the alloy casing had worn out of round. So I drilled it out to 10mm and then sleeved it before greasing and refitting.
Next up was the front door lock pull knobs, which have a shitty little plastic connector on the end that always breaks. Both front ones had broken. Remove door trims, replace plastic connector with bound wire and refit.
Then came time to take off the old mags. During the wheel swap I noticed a leak on the back driver's side brake drum. After removing the drum I found the inside coated in gear oil. Awesome, stuffed axle seal. Still going on that one!
Apart from that it is a pretty tidy old rig. I haven't managed to find any rust, which makes me very happy. There are a few other things that need tidying up, but that can wait until after rego. Anyway, back to the shed!