We have a similarly vague law in Texas too.
I set my late fees at a $50 one time charge on $250 lot rent to be a deterrent (as you mentioned) to the tenant and to also compensate me for time and expense making the tenant whole. Parks with a $10 late fee have at least 25% of the tenants late habitually, and spinning your wheels collecting that is a waste of your time and effort. You see this in the Parks where the Owner has a "discount" if you pay on time type model too.
It's fair you need to know your judges and how they rule on this as it does vary from state to state. My business case is that I have to spend an hour printing and stuffing envelopes, taking it to the post office, sending it via certified mail (if applicable), and then taking the time tracking and preparing for eviction - $50 is an absolute insult of my time for these types of tasks and I should be charging $500. By the time a tenant complains about this and you're in front of a judge you will have a lot of time already invested to make the business case that $50 is reasonable, especially if I had my attorney doing the work.
If I was really concerned I would approach these attorneys that specialize in evictions - they can talk about the local judge's mindset on what is unreasonable and have probably had clients that fought the late fee, and can help you establish the right number.
I would not implement a model with late fees for every day tenant is past due.