This sounds interesting, but I can see a number of challenges.
It'd be easy to define the original Z as "W" - which is interpreted by LCNC as another linear axis along Z.
Based on your description, you'd be using the new W to reposition the carriage for tool changes like a gang-tool lathe?
Assuming that's the case, one slightly tricky part - depending on your coding/cnc skill - will be setting up tool change macros. You'll probably need to remap "T" to a macro/ngc file that moves X & W for each tool. Idea being you never command the W-axis directly in a program - only during tool touch-offs.
You might also want to reconsider leaving the original spindle/head unpowered, presuming it still has the OEM spindle bearings and you've basically just stuffed a bushing in the spindle bore.
Without a rotating guide-bushing you will be limited to surface speeds way below desired for carbide tooling - unless you add a serious oil flow system to the guide bushing. With the price of servos so cheap these days, consider powering the guide bushing with a small servo slaved to the main spindle motor. That should reduce the lubrication requirements as the bushing will be rotating the same speed as the stock.
The biggest problem I see with the arrangement is that you have no Y-axis, and thus no traditional X/Y 'frame' like that used on a Swiss lathe. Your tools will all be on the same X-axis plane so your stock/part will have to pass between the tools - again, like a gang-tool lathe.
One practical problem will be getting your tools on center. You'll have to use shims (annoying), or adjustable-height tool mounts ($$) for all your tools insead of the Y-axis like on a regular Swiss. Or home-made holders that you bore in-situ for round-shank tooling.
Related problem... do you have enough height above the current tool slide to pass stock over it and between tools? I can't imagine that little thing being able to turn more than about 3/4" stock, but tool center height is something to consider. It'll be significantly less frustrating if your center height is a 'standard' height and you can use off-the-shelf holders/fixturing.
Last hurdle... how to you plan to advance more stock once you've parted off? Traditional Swiss have an auto collet closer in the sliding head, and a bar feeder that can positively locate & move the stock forward (and back). Unclamp head collet, head slides back while bar-feeder stays put, head re-clamps. At the end of the bar the collet opens, the bar-feeder pulls the remnant out, dumps it, grabs a new bar and away it goes.
Or are you planning to run one part at a time and advance the stock by hand? If so, what's the point of the lathe? If you want some of the benefits of a Swiss (guide bushing support for floppy parts) a traveling steady rest like Andy Pugh built would get you there with rather less work:
Not trying to rain on your parade here - just some food for thought. Love the challenge, fingers crossed and all that.