Hey, I've had experience with something similar, I hated running and entered myself in a 12km obstacle course run. Before that I had never run any distance since cross country back in primary school. The following year I entered 11 of these runs my average placing was in the mid 20s (of about150+ competitors) and came 6th in one of them
10+ km a day is overkill for a 2.4km run
Although 10km runs will help your aerobic threshold, you would be better off to run a 3km distance of hill running anerobically 3 times a week. This will give you time to recover.
This is the method that worked for me
Find a good hill, run up hard for as long as you can, and when you need to stop turn around and jog back down don't worry about the time it takes you will see improvement each time by how far you get up the hill, but do use a GPS tracker to measure the 3km distance. Running up will increase your anerobic threshold whilst strengthening your legs and jogging back down will help you recover ready for the next run up.
Also learn how to run, when I learnt how to run properly it made a huge difference to my endurance, if your running mechanics are shit you will be wasting a tonne of energy.
High soled running shoes ,(pretty much every running shoe that is not a minimal shoe) can f*ck with your footstrike, causing your heel to hit the the ground first acting like a brake. To get out of this habit I started running in bare feet for a while, because when running in bare feet it forces you to land fore footed and eliminates heel strike.
In short, run up hills try it for atleast 3 weeks and then try a 2.4 on the flat. you should see a noticable difference in your running time , learn the mechanics of how to run properly, minimise training for better recovery.
My 2 cents