What is the difference between 後ずさった and 後ずさりした as an example, and the difference between past-tense-form-verb and masu-stem-verb + した as general ?
It's quite hard to answer, so I played at some "corpus linguistics".
I searched on BCCWJ corpus for usages of single verb あとずさる and the combination of あとずさり + [0 or 1 particle] + する. That corpus contains 100 million-ish words from various written materials during 1980s to 2000s.
I got 166 samples of single verb, and 176 of する-compound (some error entries cleared).
Age (writer's year of birth)
Relatively speaking, あとずさり + する seems to be more frequently used by old writers, while あとずさる is more popular among recently born people. The percentage apparently has reversed during WWII. Of course, too young or too old people are small in number because of narrow time range of this corpus.
(The rightmost "0" column represents "unknown".)
Men use あとずさる about as many times as women, but somehow twice as many in あとずさり + する. I'm pretty surprised as I didn't expect such a clear gender distinction.
(Yellow pies mean "unknown".)
Other not quantitative observations
あとずさる appears more in simpler expressions within its own conjugation, such as plain present, plain past, independent te-form etc., whereas あとずさりする is more likely to form complex predicate, as あとずさりしていく, あとずさりしてしまう, or あとずさりして～する "do V stepping back" kind of adverbial expressions.
From context, あとずさる seemingly focuses on the doer's internal will or intention reflected on their action, and あとずさりする is more like the movement of backing away itself.
Modal expressions can be used together with あとずさりする, such as あとずさりしたい, あとずさりするつもり etc., but no results with あとずさる in the range of the corpus.
Negative forms are very rare.
A few causative forms seen with あとずさりする, but not あとずさる.
Though the answer couldn't be called well-organized, I hope it would be some help.