Your motor has a total step of 600. It means, for a complete revolution, you have 600 steps. Hence the resolution appears to be 360°/600 = 0.6° per step. This is the resolution in what is called FULL MODE.
However, your motor can works in STEP MODE 1/8. That means that you can move the motor by 1/8 of a step. Hence, you can achieve 8 more steps and thus ...
As I commented on the question, you're probably better off with conventional relays given that:
their cost scales better as you go for larger/more powerful motors
they are less complicated (since you stated that you've never
designed a circuit before)
Having said that, if you wish to pursue the solid state approach then you're probably aiming at (MOS)FETs ...
Comparing the specs of the two motors side-by-side, there are some significant differences:
Model 17HS13-0404S1 datasheet
Model 1704HS168A-OB datasheet
Both are standard NEMA-17 size mounting plate.
Both are bipolar connection.
Both are rated for 12VDC operation.
Specification | Model 17HS13-0404S1 | Model 1704HS168A-OB |
Amps/Phase | ...