[Python] Using C-IRIS or IRIS variants to decompose C-free while ignoring <mimic> joints

I previously asked about modeling a 2-finger gripper as a 1-DOF system in Drake:
How to make a gripper with two fingers (2DOF) have 1 DOF making one finger symmetric to the other.

My gripper had two fingers (each with a prismatic joint) and I wanted to represent it as a 1-DOF system in Drake. The answer provided indicated to use the <mimic> tag in an SDF file to achieve this. However, this approach does not reduce the num_positions() in the plant, meaning both finger joints are still considered in the configuration space.

Now, I am working with C-IRIS to generate convex polytopes and need to ensure that the gripper fingers are treated as having only 1 DOF in configuration space while still considering collisions correctly.

The right finger is not an independent variable and should move symmetrically to the left finger. C-IRIS should account for collisions involving the right finger, even though it is not explicitly controlled.

How can I make C-IRIS ignore the redundant DOF when computing convex polytopes?

At the same time:

How can I ensure that collisions involving the right finger are still considered, even though it follows the left finger's motion?

Any guidance on handling this in Drake would be greatly appreciated!

I am using the python bindings with Pydrake version 1.35.0

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