In Tosefta Sotah 11:7 the verses from Genesis and Samuel are discussed. It is concluded that the prophet Samuel meant that the group of prophets that Saul will meet are right now near the tomb of Rachel around Beit Lechem, but Saul will come across them when he comes to Tzeltzach. I.e., by the time he gets there, they'll have reached Tzeltzach as well.
As for Ramah, in Seder Eliyahu Rabbah (Desheh Edition, p. 332, likutim no. 42) it says:
"דבר אחר, לפיכך קברה בדרך אפרת, לפי שאפרת היא רמה..."
"...Another option, because of this he buried her on the way to Efrat, because Efrat is Ramah..."
There are various other explanations, but as you requested only Chazal, I limited this answer to Chazalic sources.