Does your current t'stat, have the thermometer in it ?
Or are you dealing with a remote thermometer?
Very often t'stat operation is subject to the location of the t'stat in relation to A/C vents. Could be nice and cool at the t'stat and not comfortable where the thermometer is or, where you're sitting.
Sorry just re-read your post , you said " keeps running " missed that.
99DSDP 3884, Freightliner, XC, CAT 3126B, 300 HP /ALLISON 3060
2000 Caravan toad, Remco & Blue Ox.