firstly the area is around death sea which is nearest as well as ,as you have said lowest part of earth .both are correct
on the same location ,all the four things happened
1.Romans defeated by Persians
2.Romans defeated Persians
3.Romans defeated Muslims
4.Muslims defeated Romans
I do not see why you have brought 4 events into play when the verses we are speaking about are only referring to 2 (the incident with Rome and its opposite).
The story of the Roman/Persian war is the common one spun out in explanation of the verses. But, as can be pointed out simply, this is a wrong reference as the believers are referred to as part of the conflict - not the pagans or people of the book. Also, the Roman-Persian war is a series of wars that lasted 26 years (602-628) and was fought in many places from Egypt to Turkey, so it cannot be described as 2 battles which is what the Quran is speaking of.
Going back to history, you would agree on the Battle of Mutah in 629 and that it was fought against Rome with the result of the Muslims being defeated? I also gather you would agree it was fought near the Dead Sea? If so, then we have part 1 of the verse matched with a historical context.
If we are looking for part 2 (the opposite event), I quoted the battle of Tabuk while clearly mentioning I have not seen any physical evidence for this. You have quoted the Battle of Yarmouk in 636 which is where the Muslims defeated the Romans (with physical evidence). I accept your quote as being the more accurate and therefore is the part 2 event which compliments part 1 and matches 100% the verses we are reading.