Word(s) for "Workflow Optimizer"

One possibility is Business Process Consultant.

However, a long time ago, such a person would be referred to as an Efficiency Expert. The term came in for a certain amount of derision, and fell out of use, but it could be used in a self-deprecating way that might appeal to some people. It couldn’t be used in written communication, but in conversation, it would be like psychologist calling himself shrink. It gets across the idea that the speaker is not afraid of the negative stereotypes of their profession, which for the right type of speaker can be a very strong statement.

There’s a charming novel called The Efficiency Expert by Edgar Rice Burroughs (better known for Tarzan of the Apes and John Carter of Mars). The humor is a little dated, but some of the situations could have taken place yesterday.

The term Business Analyst has been around for at least thirty years now, but there are still companies like this one advertising vacancies with that title.

The point is that a Business Analyst can perform any task of this nature beginning with the evaluation of current procedures, carrying on to make recommendations for minor changes or going on to full Business Process Re-engineering.

There may be people whose job title is Business Process Engineer but, by background and training they will probably be Business Analysts.

Business Analysis is quite a good descrition of the work done by both people in the question although Peter might well be described as a Process Engineer since he is more likely to be a qualified mechanical or electrical engineer.