It sounds like your 727 is a 66+ model with lever shift, since I think that change coincided with elimination of the parking cable. I doubt you can easily connect your cable shift to work with your tranny's lever shift. As oldkimmer says, look at an aftermaket cable (Lokar, etc).
There are cable-shift 727 for small block (I have one). They usually go for ~$100. To use it, you would just need the spacer ring to slip over your torque converter snout, or change the input shaft to the later type and use a later torque converter. With a 360, you need balancing weights on the torque converter. One neat thing about the early 904 & 727 is that you can push start the engine since they have a rear pump. In reply to an earlier post, there were 727's for the slant six, in taxis and trucks, though I don't know if cable-shift versions.