Sure. The US military has done this for decades to prevent brain-drain around emerging technologies to the private sector.

They could make them plain old Lieutenants for that, yes?

Distinction without a difference. They're advisors.

Then why do they need the elevated rank?

I have a dumb question but is it possible to arrange exec-tier or at last officer-tier pay for something like a private?

No level of normal military pay is gonna be meaningful to these folks, at any rank.

They're right above Privates, so still no one (of consequence) is taking orders from them.

What? Per https://www.army.mil/ranks/, they outrank all enlisted and warrant officers, plus Second Lieutenants, First Lieutenants, Captains, and Majors.

Only full Colonels and the 1-5 star Generals outrank them.