I had a look at various travel & backpacking sites, forums, & YouTube channels, to get an idea of what approaches to laundry while travelling are out there.

My previous approach of “I’ll take enough stuff that I don’t need to do laundry” won’t work with what I have planned, so it comes down to how many ‘days’ of clothing to take.
Some folks advocate for a very low number, to minimise the amount of stuff being lugged around.
I know someone who does conventions with three changes of clothes, so that one can be worn, one is ironed & ready to wear, and the other is drying in the bathroom of the hotel, having been washed in the sink.

I’d had the idea that I could try a couple of weeks worth of clothes, and if it turned out that this was too many, I’d figure it out in New Zealand, so I could just post the excess home. Wasn’t sure what 14 days of stuff would look like, so I got out the pack and did a test with 7 shirts/socks/underwears.
Figured I’d then add another 7.

Well, that answered the 7 or 14 question, didn’t it?
Things could be stuffed down more, but not a whole lot more, and doubling the amount would just about fill the central volume of the pack. There’s an extra bit at the bottom, and a top compartment, but … It doesn’t seem like the best move to fill almost the entire volume with clothing.

All in all, a good result, I think, and it fits in with this very valuable piece of advice;