Water-filled boreholes in cold ice refreeze in hours to days, and prior attempts to keep them open with antifreeze resulted in a plug of slush effectively freezing the hole even faster. Thus, antifreeze as a method to stabilize hot-water boreholes has largely been abandoned. In the hot-point drilling case, no external water is added to the hole during drilling, so earlier antifreeze injection is possible while the drill continues melting downward. Here, we use a cylindrical Stefan model to explore slush formation within the parameter space representative of hot-point drilling. We find that earlier injection timing creates an opportunity to avoid slush entirely by injecting sufficient antifreeze to dissolve the hole past the drilled radius. As in the case of hot-water drilling, the alternative is to force mixing in the hole after antifreeze injection to ensure that ice refreezes onto the borehole wall instead of within the solution as slush.