So I'm thinking more about the idea of a rotary attachment.  One part to work out is what step resolution we need.  

If the maximum diameter object we could ever machine is 90 mm then doing a bit of math we can work out that the circumference of that object is 3.14 * 90 mm = 283 mm.  If we used a smaller object the circumference would be reduced as well.  For example a 30 mm diameter would give us only a 94 mm circumference.

Our existing linear axis has a full step resolution of 25 steps per mm, with 16x micro stepping that is increased to 400 steps per mm, but we probably don't retain anywhere close to that resolution between errors caused by backlash, flex, and inconsistencies in the micro stepping.

The stepper motors we are using are standard NEMA 17 motors with 1.8 degrees per step. Again with the math that is 360 deg per rotation / 1.8 deg per step= 200 steps per rotation.  With 16x micro stepping that is increased to 3200 steps per rotation.

If we don't use any gear reduction then at 90 mm diameter we would have a resolution of 200 steps / 283 mm = 0.71 steps per mm, with micro stepping that is increased to 3200 steps / 283 mm  = 11.3 steps per mm.  Compared to the x/y resolution this is 35x lower resolution!

To match the X/Y resolution we can use a 35:1 gear reduction, that will take something like a worm gear or planetary gear to achieve, and it may not be worth it if there is too much backlash in the system.  More than 0.05 degrees of motion would nullify any benefits, that would take some tight tolerances.

We could use a belt drive, that is a popular choice.  The largest off the shelf belt drive setup I could find was 60:20 teeth or a 3:1 reduction. That would increase our steps per mm from 0.71 to 2.1.  That is still 12x lower resolution than the X/Y axis but it is better than the default. Again we need the belt to have relatively low backlash and flex or the benefits are lost.

If we just focus on lasers then we need a minimum of 0.1 mm resolution to ensure that we can draw one laser line directly next to another (assuming a 0.1 mm kerf).  Doing a bit of math that requires a 14:1 reduction if we are trying to use full steps, If we rely on the 16x micro stepping then we don't need any gear reduction at all, but that assumes 16x micro stepping is really 16x, chances are that is a bit of a stretch.

There are many different types of gear reductions we can use.  

• The obvious candidates are a toothed belt drive or standard spur gear setup.  These both can be 3D printed (minus the belt) and could easily be built into our support structure.  On the down side the reduction is low if we don't chain gears together, probably no higher than 4:1. In addition it can be difficult to control backlash, especially with 3D printed parts.
• A worm gear is a great candidate.  They can have much higher gear ratios (14:1 is easily achievable), and the backlash is relatively low.  By using a duplex style worm we can adjust out the backlash completely, at the cost of some additional friction.  But since we are not moving quickly the friction is probably not a big deal. On the downside the worm gear has higher friction, the gears are not as simple to print as a spur gear, the setup can't be back driven, and the motor needs to be set at a right angle to the chuck.
• A planetary gear will also give us a large reduction with minimal backlash.  However there is even more friction (and more backlash) in this setup.  The big benefit to a planetary setup is that it can be made very compactly.  We don't need that in this case.
• In the more extreme and exiting we can use a cycloidal drive, also known as a wobble drive.  These have a high contact area so they are relatively strong. However you need many bearings to make it work smoothly.
• Finally we have the truly wacky harmonic drive also known as strain wave gearing. This also has a large gear reduction, low backlash and a relatively compact design.  The problem again is that we need quite a few bearings to make it run smoothly.  This is very intergang but it requires relatively close tolerances to make it work.  On the upside we can get very high gear reductions with almost no backlash.

Anyway this is just exploratory work, there is still quite a bit left to go.