Keep in mind that this is a 2 cable system. As you noted you have the remote control cable that goes from the remote control lever to the engine bellcrank shifter, mounted on a bracket on the engine. Then on the other end of the bellcrank is the transom shift cable, that goes through the transom mount to the outdrive.
When doing a Cobra shift cable set up, you start with the outdrive off.
First you want to measure the drag of the transom shift cable. If it is more than 2.5 lbs (I use a fish scale with the cable disconnected at both ends both the engine bell crank bracket and the pivot housing bellcrank) then you need a new cable. If not the cable you have is still OK.....
For both parts of the adjustment procedure, there are updated factory manual instructions on Midnight Wolf's OMC parts website. I suggest you take careful look at them to understand what is involved.
So starting with the drive off:
Make sure the bellcrank in the pivot housing is able to move freely, they can get deposits built up behind them and that can limit the range of motion. I clean it out every time I remove the drive and pack the area with OMC triple guard grease to keep water out...
You then use the special tools (bellcrank in the pivot housing holder, holds it at 90*) and the shift cable tool that is used up on the engine side, that helps set the length of the cable. After that adjustment is done, you install the drive.
Then you have to adjust the remote cable and for this you need a helper, that can spin the prop (KEY OUT ENGINE OFF) while you shift the remote shifter at the helm. You need a helper to feel if the cable is getting equal throw in both fwd and rev and the prop is locking in, in both gears when shifted. This is something you can feel while spinning the prop when someone shifts the remote control.
Once that part is done you have to make sure the ESA system is working and the engine idle speed is about 600 rpm. When activated the ESA drops the rpm from 600 to about 450 so the engine must be in good enough tune, to not stall at that rpm at least momentarily. NOTE: contrary to what people think, the ESA is supposed to activate ONLY when shifting from in gear (FWD or REV) to neutral. This is to allow the clutch dogs to release the FWD or REV gear. NOT when shifting into gear.