My first K-F car back in 1975 had a problem with the overdrive governor not kicking in at the proper speed as yours seems to be doing. I found that because of non-use, the mechanism was stiff and it took some time driving it on lesser traveled country roads with various hills to get the mechanism back to regular operating mode. Also, the 28 mph figure is an approximation, coupled with the inaccuracy of your speedomer. Here's what I did as a diagnostic:
1. Several runs on a measured mile at 30, 45 and 60 mph to verify the degree if inaccuracy (the 1951 Frazer I had was 12 mph high at 60). I found the o/d working around 45 MPH actual speed.
2. On a not so busy country road with hills do some driving where the car can engage/disengage via kick-down switch at around 30-35. It took several tries but finally the o/d engaged at around 35 mph actual.
THIS IS WHAT WORKED FOR ME AND THIS PARTICULAR CAR. WHAT WORKED FOR ME MAY NOT WORK FOR YOU. ALSO, TRY THE DIAGNOSTIC FOR OVERDRIVE ISSUES IN THE KAISER-FRAZER FACTORY SHOP MANUAL FOR YOUR CAR for possible supplemental info on the problem that the Borg-Warner book does not offer as the situation may be K-F specific.