I agree with you DeAnno, but I also think scripts like communitas map (where I see bigger river networks compared to other maps I play) made Songai more powerful, as not only it allows you to move into hostile territory unhindered, you might even move better than the owner of the territory itself! This is quite noticeable in the early eras where there aren't many road networks available, or not so extensively at least, due to gpt/worker availability, as it helps attack others and defend yourself.
This also means you can defend your territory without building any (or barely any) road networks for defensive purposes (roads you would never build another civ probably), and that you can't have your mobility reduced by road pillaging.
While I think this is the big advantage of civs that have an UA that is terrain based (and that's ok, mind you), I feel Songai kit is probably the more well rounded and versatile compared to other terrain based civs, like incas, iroquois, or mongols (with horse archers for war), as this means they are the most flexible terrain based civ. They have an UA that not only serves war mongering purposes, it helps with early era expansions, with easier city connection and saving you up a lot of GPT (this is comparable with Iroquois though, but I think Iroquois are honestly just as strong as Songai in most cases unless you get a bad map script, it's just Iroquois AI is not quite as aggressive as Songai). On top of that, their UB is also one of the most powerful, as it will snowball you on already good starts with plenty of rivers and is available quite early on. Finally, the fact that rivers (unlike woods) cannot be removed makes defending yourself against Songai quite the hard task, and will probably mean you'll have settle and fight in places you usually wouldn't, this is quite similar how Icans are with mountains or mongols on very flat terrain.
I think siege units moving fast is just a small part of what makes songai AI so good, the gpt saving+early connection for more happiness+aggressive AI and good UB+UU makes a very powerful combo that is availbale early on and on most map scripts (rivers are almost always present near capitals), this means "latebloomer" civs can be taken out or heavily hampered early on (a horseman on a river can pillage a lot of tiles), something that has quite the snowballing effect.
Maybe making Tabya give +1 hammer if the tile adjacent to the river is improved (instead of unconditional +1) could stop the snowballing a bit at the start. Not much I can think of aside from nerfing mandekalu so songai isn't quite as powerful, but it won't change the fact that fightning songai near rivers is quite dreadful, mandekalu or not imho.