Hi Richard...
I can offer a few ideas.
Kiawah #4 - Sounds like you might need to - for the time being get back to basic blocking and tackling. (I have to do this from time to time myself). From what you wrote, you are quite preocupied with getting a Brtdie here - and for that reason you are flirting too closely too often with the sandtrap - and ending up Bogeyng instead. It's "Killing your card" (your words.
I recommend a half step backwards. For right now focus on getting PAR here. Put the Birdie idea out of mind for the time being. Aim your approach left of the trp at the fat part of the green and get consistent with 2 putting it. Take your par. Occasionally you will sink the longer putt and get a Bird. I know that sounds like WGT 101 but sometimes I have had to do it myself to right a slump on a particular hole.
A consistent PAR will eliminate the "killing" of your card. Once you have that going then maybe fool around with Birdies again.
Kiawah #5- I have had a degree of success getting the ball to stop to the RIGHT of the hole - along the back Fringe but still on the green maybe 18-25 feet most of the time - and alot closer than the all too common roll all the way to the back that you describe (and that I have done a million times myself. Depending on your gear, you will have to experiment with this a little bit. Too far to the right front of that green and you will have a 35+ snaking double-breaker so this takes some finessing to get used to. I am currently working on getting this shot consistent myself.
One more thought - I hope I do not throw poison in the well with this idea...have you experimented with a different golf ball? Both of these shots would be helped by a ball with a higher Spin rating.
Those are my thoughts...Good luck working through your slump on those holes, AtlantaCoaster