does it make sense to use a 4x4 radio with omni antenna at the headend, i.e., does 4x4 mean that it can simultaneously talk to 4 remote AP's at once?
No. I forget if MU-MIMO beam forming requires a single extra radio chain or an extra radio chain per client. But you certainly won't be able to send traffic from a 4x4 headend to 4 clients simultaneously.
I also wouldn't use an omni in this case as you only require 180 degrees of coverage (not 360). Look for a patch/panel/sector antenna that provides you a more ideal coverage pattern.
The alternative would be to deploy multiple gateway radios with directional antenna at the main building...
This would be my preference for this situation. This provides a dedicated connection to each downstream location. It also means a failure at the head end disrupts the network to only one location and not all four.
Additionally, you said:
2x2 radios with directional antenna on the remote buildings
I would be concerned about this setup as you can easily run into performance issues. In a point-to-multipoint setup like this, the clients would not be aware of each other, so you would likely run into the hidden node issue and possbly need to implement RTS/CTS. Without proper configuration, you could have worse performance than you have now with your current equipment.