I think SAPs are just too small to be safe with bichirs, except maybe those small Polypterus palmas polli or even ropefish. Years ago, I kept a single SAP with a subadult Polypterus palmas polli for a few weeks and had no problems, but certainly not long enough to make any meaningful statement about their compatibility over the long term.
If I were keeping SAPs with cichlids, I'd tend to keep the SAPs as the midwater fish and then various dwarf (or at most krib-sized) cichlids at the bottom, making sure the cichlids had plenty of cover. SAPs don't like going into thickets of plants or wood, or rocky caves, so the cichlids would have "personal space" they could retire to away from the SAPs. Conversely, dwarf cichlid aggression tends to be limited to the bottom six inches or so of the aquarium, so the SAPs would be ignored provided they learned to stay out of the danger zone.
I have personally kept SAPs with Mikrogeophagus ramirezi and Pelvicachromis taeniatus and had no problems with either. Dwarf cichlids usually stand their ground and learn which end of the SAP is dangerous, and more often than not defend themselves sufficiently firmly that the SAPs back off. In a 180 gallon tank, semi-aggressive fish like convicts and firemouths might even be possible, assuming those cichlids had enough space and water depth that they ignored the SAPs.
An oscar would simply eat an SAP. Dwarf pike cichlids might conceivably be one option, but my guess is even the smallest pikes would be at least try and eat an SAP.
Cheers, Neale
If that assumption is correct then I'd definitely recommend against keeping them with any bichirs at all. I personally witnessed a trio of smallish puffers totally destroy a reasonably large Rope Fish (Erpetoichthys calabaricus) even to the point of ripping one of its gill covers completely away from its body. Personally, I would never put any sort of puffer in with my beloved bichirs. Puffers are the spawn of Satan's loins! 
Great fish for species tanks though.
.......Maybe one day.
