Getting to Athens from Dubrovnik

a) rents a car, which one-way/multiple borders might get pricey

A $1200+ one way fee is "pricey" for me.

Its over 600 miles so you would have to pay a driver for 1200 miles of travel and their overnight expenses. My guess is $2k (minimum) , if you can find someone.

The 6 day tour at 1500Euro per person looks like a worse choice, from a financial standpoint.

Just fly.

While anyone can appreciate you wanting to go low carbon— a drive of 15-20 hours costing more than. $ 3,500 and an overnight on the road versus a 90-minute flight for under $100 — removes the question as to which one to choose.
I checked www.AutoEurope.com which is a reputable broker for the larger car rental agencies in Europe. The least expensive car rental from Dubrovnik to Athens for two days is $3,728.
It is also not likely you will find a legitimate driver who is legally licensed, insured and bonded in four different countries to transfer travelers across Croatia, Montenegro, Albania and Greece. The financial, legal and insurance requirements are just too onerous for a legit business to be doing that route. And if it’s too difficult for a legitimate business to do the route —-you know who that leaves to offer to do the route as a transfer.

If you want to do the route with a tour company over several days, that is a possibility. No personal recommendations or experience but “Intrepid Travel” is one company doing the route.

For flights, www.Skyscanner.com has airfares and schedules.

To do this overland there are currently no international trains to Greece.

However you could do it on Flixbus. As a through journey it takes 41 hours. But there is no reason why you couldn't break your journey at the change points of Zagreb and Sofia, maybe also at Belgrade, if you wanted to.
It is possible to do it by train from Split to Zagreb (Split is an hourly bus from Dubrovnik).
Then bus onwards

I think you can take an overnight ferry to Bari, Italy, and then another ferry to Greece.

To do this by land would not be for the faint-hearted. Either fly or maybe consider just going to Montenegro or Albania instead to relax on a beautiful beach.

Thanks to everyone for their suggestions. All good advice, and from any logical standpoint (time, cost, even carbon) "just fly" makes lots of sense. One-way car-rental from Dubrovnik is prohibitively expensive (and maybe impossible), and we wouldn't really learn anything that way.

Fwiw, for the moment, we are actually leaning to going by land via a supported (but mostly self-catered) tour by Ajdinis Travel, which upon further investigation has gotten pretty good reviews (though hotels may not be up to RS standards). We would never otherwise see a bit of Albania, Montenegro, and North Macedonia and their people...and coming into Greece from the North lets us see Meteora too.

Definitely not the cheapest way or the fastest way, but as RS travelers know, it's not the destination but the journey, right?

Many thanks again to all!