Makes perfect sense to me to want to remove the lower burr carrier seeing that gunk!

Looks as if (a) previous owner loved 'French roast" or near carbonized oily beans....one of the SJ's I refurbed came in that state and under the lower burr carrier was a pool of rancid gunk, it probably would've stayed in place forever as it appears coffee gunk can be used as super glue but the smell threw me off.

It all starts with removing the center bolt though, not sure if the TS was able to but it will definitively help cleaning the gap for the Allen key (dentist picks are great for such task, but a needle works too) to give the Allen key some more room to hold on to.

Not sure what Allen key you own, if not already in place get a GREAT Allen key set, they Allen key bolts have relatively small holes so you want proper sizing and proper steel to prevent creating a round hole in no time. I typically use an Allen key socket on my Wrench to ensure I have enough leverage as a J shaped Allen key does provide much leverage, if it does not move with the wrench it's time for heat and or oil. Buy the sort of tools a good car repair shop uses, they don't d*ck around with tools that deform or not perform.

When trying to get the bolt out, insert the Allen key socket all the way and try fasten it a tiny bit then try undo it, wiggling that way usually is enough, sometimes 'scaring' the bolt helps (give it a -controlled- whack over the head with a hammer) before taking out the (pencil) torch/paint heat gun.

How to remove the burr carrier was already discussed, it's the center bolt that needs to surrender first