Wiz, I haven't worked in several years but if it were me....unless I was having major health issues directly related to my MS.....I wouldn't mention it to them. As long as you're performing your duties that's all they need to be concerned with.
I can think of many industries that would watch someone with even "1-minute late" issues. Public safety, customer service/retail, production. We all know that it takes several minutes to get settled and begin actually working. Walking in the door a minute late really puts you several minutes late and could possibly affect other employees who might be trying to service several customers at once or even customers who have to wait for an employee to help them.
I think everyone is late once in a while. Things happen. Employers know this and, if you're an otherwise good employee, I think they know it and will choose their battles.
I know you're a good if not excellent employee and I'm sure they want to keep you. How do you receive your schedule? Do you copy it down or does your employer email it to you? Provide you with a written copy of the schedule? Maybe you could just alter your start time by 15 or 30 minutes. Physically change your written schedule (your copy) to show your start time earlier than it actually is. Sometimes -for me at least - I have to "see" it in order for it to stick in my mind. Good luck!