Before revision:  this is an analogue of the dichotomy for Weighted Subset Feedback Vertex Set recently obtained by Papadopoulos and Tzimas. In contrast, Subset Feedback Vertex Set and Subset Odd Cycle Transversal have a polynomial-time algorithm for any graph class with bounded independence number. We also generalize the polynomial-time result of Papadopoulos and Tzimas for Weighted Subset Feedback Vertex Set on 4P_1-free graphs to (3P_1+P_2)-free graphs.
After revision:  this is an analogue of the dichotomy for Weighted Subset Feedback Vertex Set , which enables us to generalize a recent result of Papadopoulos and Tzimas for Weighted Subset Feedback Vertex Set on 4P_1-free graphs to (3P_1+P_2)-free graphs.