The hardness requirement of 55 to 60 HRc will probably not be met using AISI 4340. In the quench and temper condition, you are looking at a max hardness of 53 HRc. This steel has excellent hardenability, strength and fatigue resistance.
In reviewing your post, I am presuming that the high hardness requirement is to resist plastic deformation during service, in lieu of wear resistance.
If this is correct, the following heat treatment specification for AISI 4340 should probably work;
1. For your application you will need to have the bar in the normalized condition for machining prior to heat treatment.
2. Heat the tool to 1525-1550 deg F and hold for 1 hour at temperature. Make sure this operation is performed in a protective atmosphere to prevent decarburization.
3. Oil quench to about 150 deg F.
4. Immediately temper at 450 deg F for 1 hour.
This temper should provide you with mechanical properties that can resist plastic deformation in your application.
If the hardness requirement must be met for wear or other reasons, you would need to switch to a tool steel like an M2 or other comparable grade. I have included a web site by Carpenter that summarizes some of the various tool steel grades and selection criteria;