MongoDB Stuck with Jumbo chunks while exhausting a shard
I was able to complete the exhaust by increasing the chunk size and removing the jumbo tag from the problematic chunks.
After getting the results from AdamC function, I found out the biggest chunk of that shard was ~148 MB of size.
After figuring this one out, the first step is connect to the config database and change the max chunk size:

use config
db.settings.save( { _id:"chunksize", value: 150 } )


The second step was to clear the jumbo flag from the relevant chunks.
This can be found in the MongoDB Documentation: Clear jumbo flag 

Once the chunks were no longer marked as 'jumbo' the balancer had no problem migrating them to another shard.
When all of this was done, I restored the chunkSize back to 64

db.settings.save( { _id:"chunksize", value: 64 } )


As I do not want that all of my chunks will be as big. when possible, I'll correct the hashed shard key on the problematic collections to create a more divisible shard keys.

Thank you AdamC, your initial guidance set me on the correct path to solve this problem.