Impossible to index front chain ring!

One idea, it does look like the cable has missed the channel it would come up through the mechanism vertically, i.e. it is at the yellow arrow but should be at the blue arrow aperture (if I'm identifying the cable correctly):

Little differences like that can sometimes make all the difference. Superglue is quite effective at tidying up a frayed cable if you need to re-route it. Twist it neat and then dab in superglue. Not too much glue tho or it's too bulky.

Double check the support screw is doing work against the plate as well.

Shimano tech doc extract:

If you haven't made use of the Shimano Dealers' Manual then give it a study. There is a kind of in-buit barrel adjuster, that outward facing Allen bolt on the top assembly. I think you would loosen it off when the cable is undone and once cable is in, tighten the bolt to add tension.