Is it worth it to buy larger stepper drivers?

It should be enough, make the machine work, then it will be much easier for you to decide if you need bigger drives.
Or in short: Move on!

I would just set all of your motors to 4.6 amps and see how it goes. A 7 amp power supply would probably be enough (should be about 8.3 amps by my 40% rule of thumb)

RMS is not "true" amps for some static amps for holding. But if yiu can test it now and its holds yout torque and it is not too hot - all is ok.

wrote:

I have one DM556 driver that is capable of 4A RMS maximum.

OK, try to get the DM860 then, preferably the 220V or 110V versions, depending on your mains voltage so you do not need a power supply for them.

Yup, those should do just fine, i have 4 installed in a big router for probably 8-10 years, still working.
Although i think after DM556, the DM860 is the most counterfeit drive, ever.
But hey, the price is very good, to bad i can not buy them as i would get at least 20 right now. I have to pay the same price for the so called TB6600 and still be happy about it!

I would just run with what you have and save your money for now. You just might be surprised!
Just because a stepper motor is rated to 4.6 amps does not mean it will use all of that in your application.

For example, yesterday I did a motor design for gantry. The motors are rated to 2.0 amps but the calculations say it will use 1.3 amp peak and 1.0 amps RMS. So if I set the  drive to use 1.5 amps instead of 2.0 amps, it would make no difference to performance. 
The calcs say I need at least 48 volts to meet my design parameters

So here is a humble stepper able to run at 60 m/min rapids and 5 m/s/s accelleration on a basic 48 volt power supply. Initially, I thought I might need servos but I have a bunch of these Sanyo Denkis on hand.