As much as you'd alter your grip upon a lat-pulldown machine, to target different areas of your back, I can't understand why you'd want to dismiss a cgbp, since the movement targets the inner pecs. Granted, a cgbp also works your triceps but they're simply employed as a supporting muscle, as you repeatedly press and lower the bar throughout the movement.
Since a cgbp is a more difficult movement to execute than a normal or wide-grip barbell press, reduce the weight upon the bar slightly allowing the inner-chest to take the majority of the strain as you slowly lower the bar. Equally, a similar movement can also be performed with dumb-bells, by holding them together at the top of the movement, ensuring that they remain together as you lower them towards your chest. Moreover, since you're likely to work with a lighter weight when using dumb-bells, you can allow your inner pecs to take the load.