Apologies in advance for posting about bicycles, but here goes...

I decided to take some play out of my Shimano Deore pedals.
No problem w/ the dust cap and 8mm nut, but could not figure out any way to move the cone.

It appears completely smooth (round) w/ no flats.
I tried:
o an awl
o various size scredrivers
both on their own and jamming them between the cone and pedal to achieve an interference fit, then rotating the pedal.
o half a hemostat
o extremely long needle-nose pliers, but access hole through pedal did not allow jaws to open far enough to encompass cone

There is not much room to work, so I don't think I can get enough of an angle to place a nail point on it and tap it 'round.

I don't have any small sockets w/ rubber lips...that might work.

Any suggestions?
(my equivalent Suntour pedals on my other bike {yay, Suntour!} adjusted fine.)

Pureheart in Aptos