If it were me, I would not run the f-body bar with the stock rear bar. How do I know? Because I ran the f-body front bar with the stock rear bar while my HA bar was on order. It handles fine if you baby it.
I was getting ready to make a left turn one day and the stop light turned yellow, so I floored it (isn't that what yellow means?). Going through the turn my car plowed REAL BAD. By real bad, I mean that I turned the wheel and the car didn't turn.
So, for safety sake, IMHO would not run the f-body front bar with the stock rear bar.