Hi Carly - Like the Highlands trail, I don't know if one physical map exists. The best option is locating as many park maps online that contains sections and printing those out - obviously not a fantastic solution. Some aren't high resolution either, ie Eagle Rock's here.
For the part that goes thru South Mtn, I ordered a laminated map from their friends org but they don't offer that anymore as far as I know.
These are the other resources I have for the trail:
Image from archive.org: