I don't have a picture, but do have your identical kayak and rudder.  My lifting handle (home made with about a 6" antler piece and thick parachute cord) is very "standard" in design. a loop of line simply runs through a sealed hole drilled through the after/upper portion of the pointy end of the stern/bow, about 2 inches "down" and 2 inches "in" - through the epoxy filled bow/stern pours. The handle lines are run inside/inboard of the rudder control cables, and the handle just flops around on top of the steering cables/rudder horns/back deck.

I have no trouble with fouling, tangles, interference. Everything seems to peacefully coexist back there.

I can tie the kayak down while it is rightside up by either tying only to the lifting handle rope loop near where it gos through the hull, or even threading the handle down under one side or the other of the steering cables.  Not pretty, and maybe slightly off-center, but works.  Or you could install the carry handle per usual, and by using a big enough through-hole in the boat, run a second permanent loop of line through there that was alread situated in the "down" position (you decide if it hangs below the lower pintle or above it - not sure at exaclty what point it might start to add drag in the water if you're worried about that).  You could use this loop for a tie down point.  Or maybe you don't use the lifting handle or loop as the tie-point at all, and tie around one of the rudder pintles? I never did that, but should work now that I think about it.

I use the handles that CLC sells on all of my boats with over stern rudders.  Easy to install with T-nuts and extra pieces of plywood as a backing plate.