Can you back the cable off anymore & the adjust the center adjuster so the actuator starts from as far down [call it back then] as possible.
Only other thing i can think of 'is' have you oriented it slightly wrong where it's screwed to the case & ended up with the arm starting to low down around the bottom so you would have to back out the adjuster to let it come around enough for the cable to connect.
In 'that' situation you would end up with the actuator worming [turning] out & therefor closer to the sprocket before it starts to lift--then when lifted [operating clutch] it runs into the sprocket.
One more try--is the sprocket correct & not with a step behind & setting it out slightly. I've seen some that look like that!!. but not genuine DT.

I forgot that bit--wheeling backwards. Can a floppy rear sprocket do something to the chain run when wheeling backwards opposite to wheeling it forwards. I dunno.
I see the cable is quite angled to get to the cable mount thingy. If its catching on 'that' can you just bend it over more in line as a quick fix.

Do you have an o-ring chain? Is it a 520 chain? Or 530 chain?

Chain could be the problem.... and if chain sprockets are out of alignment slightly chain can shift from side to side on sprockets depending on direction of rotation.

Now that's clever thinking MarkT. Good one. I would 'never' have thought of that haha.
Just hope it's not got 530 sprockets but unlikely or chain couldn't move sideway, albeit still be running close.
& lock washer probably wouldn't locate on the splines.
In light of this [& if cost is the issue] [& if it has 530 sprockets] you could shorten the spacer behind the sprocket a couple of mm & might move it over enough to clear.