You have raised several questions. I have outlined them and provided answers below.
Is it too harsh?
This is hard to for me to determine because this is a judgment call on the part of the leader. If it is truly your first offense it might be harsh, but then again I do not have any of the specifics surrounding the situation. What was the mission? What were the consequences of being late? Your leader is probably trying to get your attention and make sure you realize that FTR is a serious offense.
Should the corrective training be put on a 4856?
The best way to ensure the training is understood and executed to standard is to document the requirements on a 4856. Your leader was correct (in my opinion) to to place the information on a 4856.
Should the length of corrective training be undetermined?
Again, your leader is correct as corrective training is to be conducted until the substandard performance has been corrected.
Show up and “do what you are told”
As an NCO, you are typically only to be given supervisory duties. You should not be given duties that demean you or your position, especially in the presence of subordinates.
Show up for the duty with a positive attitude and let them know you understand the offense, accept responsibilities for your actions, and do your best not to repeat the substandard performance. Your attitude and tone will go a long way to diffuse the situation.
You may also be interested in reading other posts about corrective training.
