I agree with the above, if you want to keep the neons, maybe even the bleeding Hearts, every one of the fish on your list will, if opportunity presents, eat them.
And in the case of the Apistogramma, some (not all) on the list may present territorial issues, and size alone will put the Apistos at a distinct disadvantage.
All except the Andinoacara are soft water species from east of the Andes, the Andinoacara from west and in my anal way of thinking doesn't fit in geographically with the rest, but beyond my querky reasoning, th Andinoacara would be the one most likely to polish off any tetra smaller than something similar in size to it, and being very territorial one most likely to to kill any other cichlid it deemed a turf usurper.
In my current tank (similar in size to yours (a 180)) I cycled it with about 2 dozen 1 to 2" mosquito fish. Once I added young Andinoacara (coerleopunctatus, this species maxes out about 1/2 the adult size of stalsbergi) the mosquito fish lasted no more than 2 weeks .
I do have a couple tetras with the Andinoacara but they are comparable in size.