I also hugged the left side. Here's how I think it can be done with minimal frustration...
First of all, I can confirm that restarting from a checkpoint is ok. There is a checkpoint just as you approach the objective, which is really handy for dealing with the guards you need to eliminate.
When you start, equip your MP5SD (you apparently start with one if you replay an individual chapter) and your rock (just in case). Scan the area with your binoculars to tag everyone you can and do an occasional re-check as you advance.
Hug the left wall and advance up the canyon. You don't need to go very slow here. There's only one guy who is a problem. He's wandering in the forest near you, perhaps 2/3 of the way to the checkpoint. Just drop him with the MP5 to make sure he doesn't notice you. Nobody will see him go down.
Once you get to the checkpoint, keep going, hugging the wall, until you get to a fairly large, light-colored rock. Stop at this rock and wait for a minute or so for a soldier to walk by and drop him with the MP5. He will walk right past the rock and not see you, so you don't even need to peek. Nobody is going to see that guy die, either.
This is where you need to stop hugging the wall. Peek around the rock. There should be three guys in front of the objective. Between you and the soldiers there will be two rocks, sort of at the edge of a drop-off. Wait until the guys are not looking and move towards those rocks, then go prone. At this point you should be able to pop up and get a good view of the area in front of the objective. Wait until the guys are clustered together and drop them as a group. On easy difficulty they'll go down with just a bullet or three, so you can get all three with one clip. Now you can just grab the objective unopposed. Alternatively, you can try to use your rock to lead one or more of the guys away for a kill, but I did not need to do that.
I'm assuming that the guards always move in the same pattern, obviously, but I'm pretty sure that this is true.