65 cuda 273 to 360 tranny hookup

Bob's right. A 727 converter won't work. It needs to be balanced correctly for the external balanced 360. Either by using a converter that has 360 balance weights on it or using a neutral balance converter and a B&M flex plate #10239. Also it has to be the correctly splined converter. Up to 67 they were 18 spline and after 67 they were 27 spline. How well it's going to hold up is a guess. If the rebuild is fairly new and it has a good quality shift improver kit it should last a long time. If it's been awhile since the rebuild and don't have a shift kit I'd pull it and refresh it and install a shift improver kit.