Joseph,
Using the survey distance might be OK if your slopes are short, not very steep and you aren't trying to be very precise. If otherwise, it won't work.
Let's take an extreme example.
Suppose total HD is 2,600 ft. as shown on the survey. But your first half, 1,300 ft. HD is on a 45 degree slope and the last half is flat. And your error at the end of your run is 50 ft. off to the side.
On that first half you would actually measure out 1838.5 ft.staking every 100 ft., then 1,300 for the last half for a total distance of 3138.5 ft.
2 ways to go from here, both wrong.
1. You prorate the 50 ft. error over 2,600 ft. as shown on the survey and start offsetting every 100 ft. The first 100 ft., you offset from your line 1.36 ft., the next 100 ft. you use 2.72 ft. etc., adding 1.36 ft for every 100 ft distance. Instead of 26 stakes you set 32 and you have set 42.16 feet off to the side, not the 50 feet of error you had.
2. You prorate the 50 ft. error over the 3138.5 ft., offsetting 1.6 feet for every 100 ft. distance. Let's say you start from the end of you line, the flat portion. At 1,300 ft. you have offset 20 ft., not the 25 you should be half way out. So your final line is crooked, 5 feet off half way out.
Calculating horizontal distance really isn't that hard. Just take notes as you go for each segment, recording slope distance & slope. After you run your line, you'll want a break anyway, so kick back with your favorite beverage and take 10 minutes to figure the HD for each segment. Now you know the actual distance for each stake. Prorate your error for each stake (not using the 100 ft. you measured on the ground, because that is SD) and go out and set your very accurate line!
BTW, I used a uniform 100 ft. for each line segment because it is easy for examples. When actually running the line, just measure the segments you actually have, so one segment may be 75 ft and the next may be 150.