The choice of push or CRF is a personal one, but the criteria must be, "Does it work, does it work every time, and can you make it fail?" If it works it is without complaint, if you can make it fail, that failure needs to be understood and resolved. If the action is not smooth, some polishing might be in order, and seeing as how this is a custom job anyway, special attention should be taken to ensure the action is true. If the factory bolt handle smacks your shooting hand when the rifle recoils, it should be exchanged for a straighter one.
The magazine would be converted to a steel hinge floor plate if it is not one already.
Because synthetic stocks work so well, for hard use I would choose a McMillan fiberglass classic stock with a cheek piece for your custom rig. The color could be of your choice, and some folks like a pattern painted on their stocks. I would have the stock glass bedded with the bedding material extending forward to the chamber area of the barrel, then free floated to the fore end. I would add visible cross bolts installed and have pillars installed at the action screws. The swivel studs would be glued in so they don't turn and I would put the front swivel on the radius of the fore-end so the barrel carries lower, to avoid recoil cut of the hand, and to allow slinging up which should not be done with a barrel mounted sling. The sling would be a Galco Safari Ching Sling. I am partial to Decelerator recoil pads. LOP should be such that the scope ocular is even with the rear edge of the cocking piece while providing a full image across the power range, and the bolt can be easily worked with the rifle at the shoulder. If you find that your knuckle is hit by the trigger guard when the rifle recoils, have a nylon adapter placed behind the trigger guard to direct your finger downward and away from the guard.
I would choose a non-fluted Krieger #3 contour CM barrel with a diameter of .63" at the muzzle, finished with a recessed crown at 22". The front sight would be the barrel band type, I like the Ruger, but NECG's is equally good. I will deal with the chambering later.
Adjust the trigger to break at 3 pounds with no creep. Polish or replace with an after market trigger only if required.
Install a Picatinny steel base as this provides the greatest range for ring placement and eliminates the need for choosing weaker extension rings. Install a NECG peep sight opened up to a ghost ring specification to be used as either a back up or as the primary sight. Install a front post sight made of brass that is regulated to the height of the ghost ring. Mount a Leupold 1.75-6X in lapped Warne Magnum QD rings.
The part that doesn't much matter is the choice of cartridge. Many cartridges are suitable for hunting medium to large big game. My preference would be a .30/06, but anything from a 6.5X55 to a .375 would work, although some thought should be given to a heavier contour barrel should bore diameters exceed .30. Generally speaking the bolt face can be altered as required. Probably you have a favorite bullet, and I would have the throat cut to match that bullet seated to the optimum length, meaning that it does not seat any deeper into the case than necessary to feed through the magazine.