From what i've gathered.. 'Sapote' was derived from 'zapote', which itself was derived from from the Nahuatl word "tzapotl" - roughly translated into "soft, sweet/edible fruit"
You're correct in the fact that the Mamey, Black and White Zapotes are genetically not related, yet having never had or even seen one myself, i would imagine the recipe would be relatively the same. They are all 'zapote' by defintion, but Mamey is the only one with related species in the same genus
I imagine the initial sugar content and flavor palette would vary dramatically between the fruit varieties, but i would still start with 6-7lbs of fruit per gallon on the first batch - and adjust the amount of fruit in the following batches if the potency of the fruit flavor was too strong/weak.
If i'm thinking the right kind of "dry" (a lack of juice within the fruit), you could try extracting more of the flavor profile by boiling some water and pouring it into your primary fermentation bucket, over the fruits - allowing them to steep before you start the fermentation process... (I really wish i've ate one of these fruits) Might be something to try with a single fruit first - i dont know if there are any bitter characteristics to the flavor profile of the Mamey, but steeping them might accidentally bring that flavor to the forefront... It might not though, and you may achieve a larger flavor profile with less fruit...
Just some thoughts, hope to help...