The turret axis/rail basic switch doesn't work because of the cargo auto-pull function. You will are currently limited to automatic transfers between just 2 entities. There doesn't seem to be a way move cargo between a chain of 3 or more entities. Since you now have a 3 stage salavger turret, you are now at a 4 entity chain. Auto-pull is a non-starter because of this.
There is a slight workaround: Try making your turret's cargo bay into "Personal storage" in your inventory screen. You can then open your ship's cargo bay, click the "Cargo button" on the inventory screen to switch to the turret's cargo, then move everything over. It adds an extra step to the process but it's nothing that requires you to get out of your ship core. You can do everything from the same entity level.
The downside is that you can only do this with one turret at a time; which is reasonable since you can only target 2 asteroids at a time; 1 by the turret and one by you.
Hope this helps.