Z-axis stepper on delta-setup

Hello,
I’ve got a delta printer configured successfully and working.
The next step is adding an auxiliary stepper to move synchronously with Z-axis p.e. to move a “fuel tank” or filament holder.
I connected this stepper to MCU and configured as manual_stepper and can control it with MANUAL_STEPPER command. But it seems quite inconvenient since I have to inject it every slice advance and it totally breaks homing.
My goal is to move Z-stepper with standard G-Code flow by binding it to Z.
That seems like I need to create a custom kinematic but I can not clearly understand required code changes.
Do I need to create a new rail for it? Can I mix delta-kinematics of existing steppers with Cartesian one for Z-stepper?
Please help me find a right way.
Thanks a lot!