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 not longer marked as 'jumbo' the balancer had no problem migrating them to another shard.
Once 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 bigger. and 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.

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.

I was able to complete the exhaust by increasing the chunk size and removing the jumbo tag from the problematic chunks.
Thank you AdamC, your comment helped me find the required chunk size to use.

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 not longer marked as 'jumbo' the balancer had no problem migrating them to another shard.
Once 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 bigger. and 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.