Thanks so much for detailed feedback and info. In sum: mesh mode cuts bandwidth in half for 5Ghz if the mesh access points are also used for clients, because their backhaul channel is necessarily the same as their client channel. To remedy this, use back-to-back hardwired EAP225s on each end of the mesh link and disable client access to the mesh units:

router---eap225withclients---eap225noclients))  ((eap225noclients---eap225))  ((clients

Also: it turns out clients listen to each other and cooperate to limit collisions: if they hear a competing client talking they pause. If clients can't hear each other for whatever reason, they can't cooperate in this way and they collide, which jams up the AP a little. This is the "hidden node problem". To remedy this: only allow clients to share a band when they can hear each other. Mesh frustrates this aim, because again the EAP mesh architecture (perhaps suboptimally) uses the same 5ghz band for clients and for backhaul, and clients on the opposite far sides of each access point probably can't hear each other. The above remedy addresses this. But also I think another solution does too in my case (although this retains the half bandwidth problem):

router----EAP225withclients)))   (((EAP225noclients----EAP225)))   (((clients

Question: in Omada controller, how do I keep clients off of an access point?

Note: the latter approach is analogous to my current set up, which is close to 100mps, so it seems promising and slightly reduces the number of APs hanging out everywhere. 

For the record: I ended up putting an EAP225 in pretty much the same spot the RE200 range extender had been halfway between the 4th floor and 3d floor--it is now in mesh mode with the Omada controller. The EAP225 gets much better signal than the RE200 did, and provide great signal and speed to the entire 4th floor. The setup is now:

internet------router--------EAP225_clients_and_mesh )))      ((( EAP225 )))  clients