Oops, sorry.
Why did I read Santorini instead of Milos? No idea... maybe the wine...
Yes, the drive is shorter from Nafplio to Piraeus. The issues you might encounter are the morning traffic jams upon arriving in Piraeus. To allow for a minimum safety margin, I think you should leave Nafplio around 5:30 a.m.
If you can return the car to the port of Piraeus, the security procedures for boarding the ferry are nonexistent. You just need to be at the dock ready to board, say 10 minutes before the ferry departs. But be aware that the ferry doesn't wait for latecomers. It leaves on time.
The port of Piraeus is huge. There are about 4 kilometers of docks. Seajets ferries to the Cyclades depart from Gate E9, which is located here:
https://maps.app.goo.gl/G5vQjsijxcik8UkcA
Street view:
https://maps.app.goo.gl/MGfoB8VQhWDWuKyM9
If you are returning the car in Piraeus, contact the rental company, specify this gate, and arrange a drop-off location. You should be able to return the car to the docks near the ferry.
Note that on May 29th, you can also take the Minoan Lines Festos Palace ferry at 9 PM.
https://www.ferryhopper.com/en/#/results?itinerary=PIR%2CMLO&dates=20250528
Advantage: Only €44 per passenger, no more hassle with the trip to the port, no need to get up in Nafplio at 4 AM, you could spend a large part of the day strolling around Nafplio (or anywhere else between Nafplio and Piraeus).
Disadvantage: you'll be in Milos at 1 AM (hotels are used to these late arrivals).
The journey to the airport is a little longer, and you may also encounter traffic jams. You'll need to allow for some time for the procedures, which can take longer than in Piraeus depending on the rental company and the location where you return the car (finding the right parking). Then, be at the airport building at least 1 hour before takeoff, or 1.5 hours if you have luggage to check in.
All that being said, there is still an (expensive) option if you're flying to Santorini: once in Santorini, you can arrange a transfer from the airport to the port and take one of these two ferries to Milos:
https://www.ferryhopper.com/en/#/results?itinerary=JTR%2CMLO&dates=20250529
The transfer time from the airport to the port by taxi will take about 30 minutes (around €40).
The ferry ticket costs €93.70 per passenger (yes, Seajets ferries are overpriced), add the €40 taxi fare, plus the cost of the flight to Santorini.
So, 4 options. It's up to you.