I spoke with Robert Gribble just 10 minutes ago. He said that Mt. Carmel/Hollywood and Rose Hill are not affiliated.
Rose Hill Cemetery belongs to the Southwest Memphis Cemetery Association. The Director of that association is (or was) Leonard Dawson. Apparently he has not heard from Mr. Dawson in a couple years and believes that he may be deceased. Mr. Dawson is connected to Crane Creek Baptist Church. The church was once responsible for upkeep of the cemetery grounds. The phone numbers he had for Mr. Dawson are:
901-785-0084
901-948-5767

Mt.Carmel/Hollywood is Owned by Carol F. Hayes. I ran a check on her through Inlellius and found this:

Address 1:
1740 GRACELAND CV
MEMPHIS, TN 38116
(901) 332-6312

Address 2:
BOX BOC
MEMPHIS, TN 38116

Address 3:
PO BOX 161302
MEMPHIS, TN 38186

However, Robert Gribble said that he was fairly certain the following address is current:

3228 Wedge Hill Cove
Memphis, TN 381285
901-544-0849

My next step is to follow up with Southwest Memphis Association. If I learn of any information regarding Mt.Carmel/Hollywod, I will surely inform you.

Regards,
Earlene