The reason you were advised against fully changing the oil is that on a transmission with some apparent slippage, and with potentially worn friction surfaces, the contamination in the oil may be the only thing prodiving enough friction to provide clutch engagement. Once the oil is drained and clean, particle free oil is added, there is nothing left to make clutches grab. That's pretty rare at only 85,000 miles, even if it is all city driving.
Since your transmission apparently didn't exhibit any more slippage after the oil change, change it all and get a complete fill of clean fluid. Clean oil can lubricate better, help flush out contaminated valves, clean up sealing surfaces, and allows for overall better hydraulic operation of the trans.