Engine is pulled - 273 rebuild or replacement 360 crate?

The car already has headers. 273 motor mounts can be easily modified to fit a 360 (add a pie shaped piece of metal on one side, extra washers on the other. Will need to balance the flywheel for the 360, but the 9.5 inch clutch setup will bolt right up to a 360. There are HD versions of the 9.5 inch clutch available, or OP can just swap to a 10.5 inch clutch. All the front stuff from a 273 will fit a 340, but the 360 stuff will work if you move the bottom radiator outlet to the other side (used to be any competent radiator shop could do that, maybe not so easy anymore since radiator shops have all but disappeared). The 7 1/4 rear will have to be replaced, but it won't hold up to a strong 273 for long, either, so it will really need to be replaced anyway.

Since the OP's 273 isn't the original motor, his Barracuda is not a factory Commando, and the motor needs to be replaced with something, whether a 273 or larger, it to me is a no brainer to swap in a 360. That swap gives you 87 extra cubic inches. That's WAY more than a 4 inch stroker crank in a 340 or 360 gives you. Or you could swap in a stroker 360. 408 minus 273 equals 131 perfectly streetable extra cubes. Even better. And it fits anywhere a 273 will fit.

My 65 Barracuda has had a 340 in it since 1973. I was able to make the swap work before I had any tools to speak of, or any mechanical experience. Don't let anyone scare you into thinking replacing a 273 with a 360 is a difficult swap.