The main problem (as you surely noticed) is that Eorl is dead.
Dead heroes will not be added (and only evil forces have "necromantic" abilities)
Definitely not Men of Rohan. Only Durin for Dwarves is acceptable, yes, he is dead, but he is reincarnated - with him it is about legacy for Dwarves, he is powerful symbol for them.
When Rohan will have "dead hero" so Dwarvish ring hero concept won't be unique.
I think that Theoden fits very well into the role. As a wise king, who reminisces about old times. Who has respect for Rohan´s ancestors like were Helm or Eorl. And who would use the One ring to defend his people against the destruction that spreads from Isengard.