This is a pretty open 'what if' scenario, and as stated above everything depends on the specifics of each situation.
I've done similiar walks along coastline in some pretty rugged places. Three points;
1)I've always found that, since I mainly hike without tracks, somehow following a track is a sure fire way for me to get a little lost! I find that when going overland without a track you navigate fastidiously to always know exactly where you are. When following a track the temptation is just to walk and not really navigate - except for a few cursory map-to-ground observations every hour. What happens then is if you're not careful you can easily lose track of exaclty where you are. Which is okay unless the weather closes in or something else 'exciting' happens.
2) Often these coastal tracks look 'easy' on the map since they generally don't go up or down very much. However, the country you'll be going through looks like the track is at the bottom of steep slopes. What this means is that the track may actually go over lots and lots of smallish stones that have rolled down from the heights above... Suddenly this neat little flat track on the map takes on a rather tedious aspect; when carrying a pack this sort of walking can become very very slow as it's quite difficult to weave your way up and over all of these little stones because you're always trying not to have a fall and spraining your ankle- so I'd suggest allowing twice as much time for every leg than you might think necessary.
3) I've carried people solo across country and it can be very very hard depending on what the footing is like (see above), your fitness and strength, and *also* how tough the person on your back is; if they are in pain and complain a lot it's hard to ignore and makes life harder for you (you tend to wish that they were unconscious...

). Also, even a totally uninjured person can find it hard work just to be carried!
All in all I'd say your best options are to;
Given the distances involved a man jogging without weight on his back could make it out of there very quickly; the trail that took you a day to hike with your pack will only take you an hour or two if you are unladen. So, if you think you can make it out in one day dump excess food and stoves etc, take bivvy bags or tent with you and gget going! Best option is, if at all possible, make the patient walk and support them as best you can.
If he can't be moved then stabilise patient. Put them in shelter and fix them up with enough supplies etc so they will survive and make sure you know exactly, exactly, exactly where they are.
PS; my favourite saying is; "adventure begins when things go wrong", and we all like a bit of adventure right?? So don't stress when things go wrong, just view it as a new problem to solve.