Do you have a way to speed up the flow of wort through the chiller? The lower amount of time the wort is in contact with the chiller the higher the temp will be.
The homecenters sell garden hose ball valves that you can put between the hose and your counterflow. I run my wort full bore and dial the temp in with the coolant flow. However, 60F is a great temp to pitch at even if you plan to ferment in the mid 60's. Some folks here would kill to have 60F output without using ice.
You are getting an awesome cold break dropping it from boiling to 60f in a matter of seconds. Why would you want to warm it up????? But as everyone has said turn the wort flow up or the cooling water down.
I gravity feed through my chiller, so I can't speed up the flow of the wort, but what I do to regulate temp is slow down the water flow. In the summer, I can run it full bore, but in winter I was having to slow down the water to keep the wort going into the carboy right around pitching temps.