FeasRelax with smart choice of cons to drop

I'm attempting to use the FeasRelax function on a minimization problem. My problem has some constraints that conflict with each other. FeasRelax successfully drops some of the conflictors. However, I need it to do something slightly more advanced: I need it to drop constraints such that my minimization problem is maximized. I want it to keep the constraints that push up the resulting minimum the most. Is this possible with FeasRelax?

If it's not possible directly, I was considering an iterative approach where I manually adjust the penalty of the constraints given to FeasRelax to force it to keep constraints that were ignored until I can't push up the result any further. How can I tell which constraints were ignored? Do you think something like the code below should work? (It doesn't work.) Can I repeatedly use FeasRelax on the same problem like in the code below?

for _ in range(10):  # wanted loop until done
    # model.reset()  # need this?
    model.feasRelax(0, False, None, None, None, disj, penalties)  # won't work
    model.optimize()
    if model.status == gp.GRB.OPTIMAL:
        if model.objVal == last_score:
            longests = [v.X for v in vars]
            return longests
        last_score = max(model.objVal, last_score)
        chgd = False
        for c, con in enumerate(disj):
            if abs(con.Slack) > 1e-5:
                penalties[c] *= 100
                chgd = True
        if not chgd:
            print("   no penalties updated.")
            longests = [v.X for v in vars]
            return longests
    else:
        handle_infeasible(model)
        print("Model not optimal")
        return None