The description of your dilemma is a bit sparse so I must make some assumptions regarding your situation based upon my experience. Some engineering companies offer advancement in pay and recognition to exceptional technical talent who have no desire or aptitude for any formal leadership role. Their titles were generally something like “Senior Engineering Specialist.” Their office space is comparable to a manager’s. At best, they are technical mentors to the next generation of engineering talent.
Prior to establishing this alternate (“Dual Career Track”), valued technical experts of long service hit the top of their salary bracket unless they moved into a formal management role. We were losing valuable talent to competing organizations that provided a dual career track. I’m assuming your situation is similar to what I’m describing. I also make up that your situation is complicated by DoD accounting rules regarding billing procedures, etc.
In over 40 years of developing selected technically trained professionals into managers and executives, I’ve never been able to train an individual who did not deeply aspire to be a leader into being one, even a mediocre one. If they didn’t have the passion to be a leader, it is like “teaching a pig to sing.” It is waste of time and only irritates the pig.
The fact you are asking the question of how to reduce your non-billable hours with the least resistance and loss of scarce talent indicates you grasp the polarities involved in this dilemma and see no clear path forward. With a broader understanding of your culture, existing projects, etc, I may be able to help you balance the trade offs and identify the unintended consequences of your options. I’m empathetic with the discomfort and difficulties of your situation.