I do something similar with a variation dictated by the fact that the cooking flatware is kept in a different drawer than the table flatware. Since I'm the one who loads the dishwasher most times it works well. However my wife is allergic to any form of organization so when she "helps" the system falters a bit.

Sorting is a classic and very important problem in the world of computer programming. Numerous, ever faster algorithms have been developed. If you want to jump down that rabbit hole, a good start is here...

https://en.wikipedia.org/wiki/Sorting_algorithm

These algorithms are for list sorting, e.g. alphabetizing a list whereas our problem is more of a heap sorting problem. Rather than ordering the flatware by size or color, we want to create heaps of knives, forks, teaspoons, tablespoons, etc.; ordering within the heap is unimportant.

My approach to the boredom of such tasks is to not waste much time on shortening the task time but rather keep an inventory of problems that I can work on mentally while mindlessly sorting, cleaning, polishing, whatever.