This is far from being solved from my testing, I think 1678 is not the same thing.

The base issue is that the total range of the joystick axis is split in half no matter how that range is set, and there is no way to remove the + or - on the axis.

Z+ is the top half, Z- is the bottom half. (this can be reversed easily) but the issue is the same.

So, for a full analog axis configured as a slider (and reporting to Windows as a slider which is usually 0 to 255 in terms of raw output values), only half the range is used for + or -. So, Arma splits the range, in this case 0-127, and 128-255 and uses that range as axis + or axis -. As a test, I reconfigured my throttle using the CH Products tools to behave as a centered axis, reporting -127..0 and 1..128 and got exactly the same behavior in terms of the collective mapping. In other words, it doesn't matter what range the joystick reports, Arma treats it as a centered analog control. Perhaps there is a trick here, but I haven't found it yet!

The net effect on the collective is that to increase it, nothing happens until the throttle is positioned halfway to max (top half), and the same thing happens for decrease, where it doesn't decrease until it's positioned in the bottom half.

The desired behavior would be as follows:

Throttle at 0 - collective 0
Throttle moved to center - collective 50% of max
Throttle moved towards max - collective 100% of max

Increase throttle (move lever up) = increase collective
Decrease throttle (move lever down) = decrease collective

A good reference for this would be the way Eagle Dynamics implements its joystick mapping for helicopters in the DCS series. Unable to duplicate that type of mapping inside Arma.

This said, it does work using only half axes, but it doesn't feel "normal", and my sensitivity is half of what it can be.

Same issue here with a CH Products Pro Throttle. Unfortunately, the CH products programming tool does not allow mapping half axis to a full axis.

Also, I verified it is reporting in as a full slider, not as a centered axis.

It seems all axes, no matter how they are configured (centered or slider) are interpreted by Arma (3 in this case) as a centered axis.

It would be great to have the mapper have a checkbox to use the full axis, or to manually do this through a configuration file (as some other titles let you do).