I used to use theTurns Engine and MPPR to run multiple cost table passes in PAR, but those features were deprecated.
What can I use that gives me similar results?
The MPPR and Turns Engine functionality was deprecated because it was only able to vary placement cost tables during PAR, whereas placement is done during MAP for the newer device architectures. The MPPR functionality was moved over to SmartXplorer as what is now referred to as "variability passes". Variability passes can be used in different modes both from Project Navigator and from command line SmartXplorer.
For more information about cost tables and their usage, see (Xilinx Answer 35534).