Oh wow mechanical heat recovery systems have jumped in price. They were 2-3k a few years ago. The way mechanical heat recovery works is kind of like penguin legs. The inflow and exhaust airflows pass by each other. So the warm exhaust air passively heats the cooler inflow air. So they are quite basic things that are very cheap to run. I guess another kiwi tax. Done some googling for pricing and it does appear 5-6k is the going rate now. E.g. another option: https://www.smooth-air.co.nz/home/hex390
What about something like this: https://www.smartvent.co.nz/why-smartvent/ that should also improve the humidity. Doesn't say price though. They seem to have a variety of options including positive pressure which should be much cheaper than a heat recovery system. https://www.smartvent.co.nz/smartvent-positive-advance/
Here's some more information about heat recovery systems and why DVS/HRV from the attic are shit. https://www.smarterhomes.org.nz/smart-guides/heating-cooling-and-insulation/ventilation-and-heat-recovery-systems/
That should work if you bring it to the soffit instead of a different room. However youre paying extra for the temperature sensor. Don't get the air from the attic, it's not healthy air, I don't care how good the filters are, it is something unheard of elsewhere in the developed world. I would rather have nothing than air come in from the attic. Please rid yourself of the idea of venting from the attic.
I have these links saved in my bookmarks when I first researched this 10 years ago and retrofitted a ducted HVAC system in my previous house.
https://www.energyvanguard.com/blog/Case-Closed-Get-Those-Air-Conditioning-Ducts-out-of-the-Attic
https://www.nrel.gov/docs/fy10osti/48163.pdf
In many countries in Europe houses actually have to have their ventilation/insulation performance tested and pass the test (e.g. blower door for air tightness). We have gotten better at insulating but our builders still don't generally understand the importance of mechanical ventilation. Cue Mouldy homes chapter 2.
Balanced heat recovery mechanical ventilation > positive pressure ventilation > negative pressure ventilation > nothing > air from the attic.
Just my opinion. I don't work in the industry. Just a geek.