Err on the side of simplicity.

There are a number of ways you can keep the look of your writing clean, and the most obvious, easy way is to eliminate unnecessary periods.
There are two ways to eliminate periods.

1. When telling time. It is easier to comprehend, faster to type, and cleaner to use AM/PM when specifying time, as opposed to a.m./p.m. And if 5 AM is lots cleaner to the eye, it’s also so much quicker to comprehend and faster to type than 5 p.m. The advantage of using AM/PM is especially obvious when combined with other punctuation marks: Does the workshop last from 7 to 10 AM?; I need to leave at 10 AM!; rather than Does the workshop last from 7 to 10 a.m.?; I need to leave at 10 a.m.!;  As an editor, I like to keep things simple.

2. Use acronyms without periods. A good example is writing educational degrees, like PhD, MD, MBA, etc. Let’s face it: Ph.D. is heavy; PhD, not as much (though of course there is that up-and-down thing with the letters in PhD…). The advantage of PhD instead of Ph.D. is particularly obvious in the plural form (for example, PhDs and MBAs instead of Ph.D.’s and M.B.A.’s), since the “apostrophe-plus-s-forms-a-plural” structure that comes into play when you use an acronym with periods creates the exact same spelling of a singular possessive. And that, my friends, can cause confusion, so banish those periods with your acronyms!
So, keep it simple. Choose to eliminate extra periods by using AM/PM to designate time and acronyms without periods.