Should I stop and spend the night somewhere in between Monemvasia and
Nafplio or drive directly there? Looks like a 3-ish hour drive?
Monemvasia (1 or 2 nights). Visit Kyparissi?
If you arrive in Monemvasia early enough you will have time to visit it and will not need to stay in Monemvasia more than one night.
For us, Monemvasia, even if you can take beautiful photos there, was a big disappointment because of its "theme park" atmosphere where there is zero local life apart from that dedicated to tourists with its hotels, restaurants and souvenirs shops, so for us a 3 hour stop would have been enough.
A 3rd option would be to drive from Nafplio to Monemvasia via the coast and stop at Kiparissi but this involves around 5 hours of driving on scenic winding roads
Regarding Kythira..
"Spend 5-6 nights on Kythira, probably in one spot (beach area) or
split into two locations."
You don't need to change location during your stay in Kythira. By car it only takes an hour to go from one end of the island to the other.. If you choose an accommodation that you like, why go to another, waste time checking out - checking in, just to go only a few kilometers further?
By choosing relatively central accommodation like Potamos (pretty village) like tommyk5 or a little further south like us in the area of the villages of Arionadika, Frilingiánika, Pitsinades (even prettier!), you will be very well located, even to go to The beaches
In about 30 minutes of driving you will be, for example, on Diakofti beach:
https://photos.app.goo.gl/dN28JNUxeYXrJsak9
Or in Avlemonas:
https://photos.app.goo.gl/jDvdmhfHcuDvRHSg7
Some other (short) videos taken this year
The roads in the center of the island (towards Pitsinades where we had an Airbnb)
https://photos.app.goo.gl/W3rwhfPYEko8Cghe8
Easy hike in the center of the island:
https://photos.app.goo.gl/HyjEDKoaayBi7SodA
See how the Neapoli→Kythira ferry trip is done (with the car on the ferry).
https://photos.app.goo.gl/utwn7vepfS7qv1t18
Another hike from Chora, the capital:
https://photos.app.goo.gl/NKMELz161YiAWpua8