Your choices will certainly work, but only if you are careful. If you don't pay attention to the details, you will cause the power supply to go into current limit, with bad consequences for system performance.
First, your choice of driver is fine. With a 4A/phase capability, you should have no problems on that count.
Now, about the motors. The first thing you need to realize is that the 2.8 A limit applies to each winding, so it's perfectly possible to draw 5.6 A in normal operation. Since you will be running as many as 3 motors at a time, your current draw will be as high as 16.8 amps.
Is this a problem? Not necessarily. The question comes down to how much torque (and therefore current) you need. You must have noticed that you cannot apply 12 volts to the motor for any length of time, since this will provide 12 V/0.9 ohms per phase, or 13.2 amps once the inductive effects has settled out. Instead, you'll need to create (or buy, they're cheap) a constant-current driver. Commercial units use PWM controlled by feedback from a current sense resistor (which you'll notice on the L298 data sheet). In the process of building or using such a circuit, you can set the current to pretty much any level you want.
So, if you set your current levels to 1.5 A per phase, you'll draw 3 amps per motor, and 3 motors will only draw 9 amps. Of course, this will only give you half the torque you expect. How much do you need?