Well, for one thing, your C# code and the Thorlabs example code don't match what you have in your LV code. Each of them uses different classes and methods, at least for the initialization.
If you want to call a .NET constructor in LV, you need to use the Constructor Node. That said, I would suggest that you actually stick to using the UI control, because my experience with using the Thorlabs .NET code was that it was possible not to use the UI control as the basis for the connection, but that it wasn't very stable. I'm assuming that even though the classes are different, you would still have the methods you need.
Another thing which was a pain was that you need to take all of the Thorlabs DLLs and place them in the folder of your LV project (or EXE when you build that) for this to work. They have a tool which is supposed to copy just the DLLs that you need for your specific device, but as far as I could tell, that doesn't actually work.
I don't have the right stuff installed, so I can't see all of the details for your code, but I see that you do have a direction input on the MoveJog method. If you create a constant from that, LV should translate it correctly from the .NET enum to a LabVIEW ring control with the relevant values. I'm not sure why you wired 60000 to it.
As for how to handle the direction change, in LV the wires usually fill the rows of variables and you can add a shift register to a loop to pass values to the next iteration, but I would suggest just looking at the value of the loop iteration terminal. Feed it into a Quotient and Remainder primitive to divide by 2 and then you can check if the remainder output = 0 and use a Select primitive to output either FW or BW as the direction.
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