I don't know if haplogroups could be mixed in here, but L and R2 are probably the two strongest candidates for ancient Dravidian speakers that lived in the Indus region, if you go to Southeast India today R2 is very strong there among Telugu populations
today in India R1a1 and R2 go hand in hand and are strong and weak in the same communities and areas..
Mesopotamians is a general term for many different groups, I would say pre-Iranian Iran was probably related to the Dravidian speakers, groups such as Elamites and Kassites that lived in modern day Iran before the arrival of Indo-Iranian people from Central Asia were likely very close to the Indus people.
See I have a problem when people mention haplogroup J2 with Sumerians, the reason for that is because there has been no ancient DNA of Sumerians found, not to mention that the haplogroup diversity within that region today is very great with many different haplogroups. An interesting study for that would be to test Marsh Arabs, but then again I have a feeling they have a very strong Arab background and we'll end up with J1 mostly.