I don't think you should describe the accent, what you should describe is the effect that accent has on a listener.
Obviously if the listener has the same accent, then the effect is zero. (An exception; if the listener is not expecting to hear their own accent. h/t to @Spagirl comment.)
But if listener has a different accent, what about the other accent causes reaction in them? Are they mentally translating, not recognizing words or being distracted by the pronunciation of the words?
For example, as an American professor listening to Indian students, I have to make an effort to concentrate and NOT be distracted by the far more musical tones of Indian speech when the students are just speaking English. I can lose track of what is actually being said, because of how it is being said.
Sometimes foreign students will truly mangle the pronunciation of English words to the point I get distracted trying to figure out what they are talking about. The same thing can happen with accented speech. It can sound funny (humorous) to a person, or confusing, or just so wrong it is unintelligible.
In America, different regions can have different words for the same thing; like "pop" vs "soda" vs "cola". When I travel, I find it mildly irritating to have to mentally translate regional dialect.
So instead of trying to duplicate in a reader the sound of what is happening, and hoping readers will realize the same effect, instead try to describe the effect of the accent directly. Both the overall effect, and perhaps specific effects on phrases or words.