First I have never had this problem so I cant advise on knowledge.Maybe you could talk to a transmission shop guy. You know get another opinion. Get many opinions. These trannys and the V6 FWD combo have been around for awhile so I dont understand why a 96 would need a update. Maybe a fluid change and filter is in order.
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86 LeSabre Limited Coupe 3.0 litre
86 Riviera 3.8 litre
91 Regal Limited 3800 cc traded for '99 "88" anniversary edition - mistake
82 NewYorker 318 ci
75 Royale convertable 350 ci
76 Royale 2dr Hardtop 350 ci
97 LSS L67 3800cc SuperCharged