Stability conditions for sub-quotients of category O

Recently, Anno, Bezrukavnikov and Mirkovic introduced the notion of a "real variation of stability conditions" (which are related to Bridgeland's stability conditions), and have constructed an example using categories of coherent sheaves on Springer fibers. Here we construct another example, by studying certain sub-quotients of category $\mathcal{O}$ with a fixed Gelfand-Kirillov dimension. We use the braid group action on category $\mathcal{O}$, and certain leading coefficients of polynomials coming from translation functors.