My neighbor drives a 97 Dodge work van. He has the same conditions. Reverse is always there but he waits a few seconds for drive at first go. Wont go into overdrive before its warmed up a bit. Trans filter serviced once, made no difference. Van still drives today no better or worse.
Several years ago, when the trans in our 93 Lebarron failed ,
I was told that Chrysler trans coolers had strainners in them.
Back flushing that strainner is a gamble.
Replacing the cooler is best route and recoomended with trans rebuild.
I dont know how much of this is correct or if its relevant to all models.