Have one pilot who is your dedicated Maintenance Test Pilot, or even have more than one, or have a roster so the duties are shared out.
Hardly a difficult problem to solve but that wouldn't maximise profits - until an engineer accidentally gets airborne on a ground run and totals the aircraft - that would be expensive.
That might work at your government job, but as you said it wouldn't make financial sense in the private sector. Not too many companies could afford 10-12 pilots (X2) sitting around off contract.
Would you keep them flight current on one model or all models that visit the base? Or current on one model and ground qualified on the rest? If current on all models, do you pay them at the rate of the largest aircraft qualified? Etc., etc. At current pay rates of the largest aircraft (S76) mechanics ran when I left, that would cost over $1.5M USD/yr just in salaries for those maintenance test pilots to be available at 10 bases on a 7/7 sch.
That's why 50+ years ago mechanics started running aircraft over here. As for a wrench banging one up or flying away, it happened (I recall 5 in my 30+ yrs) but no where near the rate of pilots who banged up or destroyed theirs during a ground run.
Bottom-line, when the sun rose, every aircraft was ready for revenue save the odd test flight or flight track requirement. And it still goes on today except the fleets are getting smaller and changing with the 92/139 types and double flt crews reducing the need for mechanic run ups.