When it comes to getting rid of something slowly and steadily, there are several synonyms for the phrase "gradually dispose of." One option could be "phase out," which suggests a gradual decline of something over time. "Eliminate slowly" is another potential choice, indicating a gradual removal of something that is no longer needed. "Reduce in increments" or "diminish gradually" can both convey a similar meaning of slowly and steadily getting rid of something. Finally, "wind down" or "ease off" can also work as synonyms for slowly disposing of something, suggesting a gradual relaxation or decrease of something.