Hi, goldnsx.
If the aim is to complete the system at your place AND eliminate the moisture in the system AND minimise the time being spent at the shop for charging the refrigerant, then just hire a decent vacuum pump.

You can buy one but may not be cost effective unless you use it regularly.

On the other hand, even the reasonably priced manifold gauge would become handy just for monitoring the system pressure to spot any issues.

I'm quite sure you are aware of the saturation curve of the water but unless you can use dry nitrogen in closed loop industrial system, just passing it through the system won't be enough to remove the moisture even on the automotive a/c system.

As soon as you expose the parts to the atmosphere, the moisture is introduced.

With DIY flushing, you rely on the flushing solvent to soak into the debris in a hope to separate it from the internal surface.
Once soaked for a while, then you run the pressurised fast flow of solvent fluid to push it out, ideally in reverse direction as well (back flush).
Then, the compressed air (or nitrogen in your case) to further push out any remaining debris.

I don't know what benefit the dry nitrogen has over the compressed air during the above process on automotive a/c system but if you already have access to it, it won't harm.
For small refrigeration system service, I do use nitrogen but for different purpose.

The vacuum pump will lower the boiling point and evaporate the moisture inside the system.
By keeping the pump running for long period, the saturated moisture will be removed further.

Once installed all new parts and confirmed that there is no leak with the system, I normally run the vacuum pump for more than 2Hrs.

When dealing with the service of small refrigeration system, even just 5g of moisture inside the pipe takes ages for removal.
However, with properly flushed NSX a/c system, good vacuum pump kept running over 2Hr would be enough.

So, after flushing the system, start re-installing the parts and install compressor and the receiver/dryer as the last item to be installed.
Carry out leak check and then pull deep vacuum for long period.
After hours, stop the pump but keep the system under vacuum in preparation for charging the refrigerant.

I'm HVAC certified in Japan but don't know how to convert it into F-gas certificate in Europe so can't handle the refrigerant.
I just ask my friend to charge the refrigerant at my place.

For your case, just keep the system under deep vacuum and disable the compressor (not required because of triple pressure sw but as a pre-caution).
Then, just drive to the nearby a/c shop to charge the refrigerant.

This will save everyone's time.

Kaz