Small victory in the war against the Cincinnati cinturn 12u

Why not just use the built-in decoding of the carousel comp?
Set num-sense to 3, connect the switches to IO pins and then to the sense pins in HAL, wire up the strobe the same way (to the carousel.0.strobe pin).

linuxcnc.org/docs/stable/html/man/man9/carousel.9.html

The encoding is absolute. The carousel component should always know which tool is selected with no need to home.

For a lathe you probably don't need a remap, just connect iocontrol.0.selected-pocket to the carousel.0.pocket-number, iocontrol.0.tool-change to the carousel.0.enable and carousel.0.ready to iocontrol.0.tool-changed.

(You probably need to make sure that your G-code moves to a safe place to tool-change. A mill can just retract to max-Z in general but that doesn't always work for a lathe.

I don't think you need any ladder logic. But if you want to use Ladder to control the toolchanger that will work. At that point you would not need the carousel component. Do you plan to use ladder programming or use the carousel component?

For the moment I will ignore the fact that lathes normally change tools with just a T command not an M6.

When LinuxCNC encounters a T command it puts the pocket number on the pin iocontrol.0.tool-prep-pocket and sets the pin iocontrol.0.tool-prepare

The tool changer logic is expected to monitor these pins and act accordingly.

When iocontrol.0.tool-prepared is set to true, execution continues.

It is very common to connect these two pins so that execution passes straight through while the changer is selecting the next tool. eg:
When LinuxCNC sees an M6 command, it pauses and sets the pin iocontrol.0.tool-change and waits for iocontrol.0.tool-changed to go high.

So, you use iocontrol.0.tool-change to activate the carousel motion, and when it has done its thing, you use carousel to set iocontrol.0.tool-changed, and programme execution continues.

With the HAL connections here your G-code would need t use the M6 Tnn G43 combination for each tool change. Using T-only needs a remap and is probably best handled later.

Seems you have in hal:
addf conv-float-s32
But there is no :
loadrt conv-float-s32
Try adding the last line in hal, before the addf line.

The conv instances are numbered (starting at zero)

linuxcnc.org/docs/stable/html/man/man9/conv_float_s32.9.html

Try