There are several alternative words that can be used instead of "regimentally" to convey a similar meaning. Some of these include "methodically", "systematically", "disciplined", "rigorously", and "orderly". Each of these words emphasizes the importance of structure, organization, and adherence to a set of rules or guidelines. Whether describing a military unit or a personal approach to achieving goals, using any of these synonyms can help to convey a sense of concerted effort and an unwavering commitment to achieving success through hard work and determination.