There's actually quite a bit of work out there...but people are looking for experienced guys in Falcons/Gulfstreams/Globals....I have also seen Aviation Manager position in similar equipment. I have talked to people very recently who simply cant find qualified people, as they want experienced International PICs in the above aircraft...current or not.
I would suspect the issue may not be your Boeing time, but more likely your location and your lack of desirable ratings?
I would also NOT have 2 resumes. It would not be good to dig up stuff during an interview...like that you were hiding being a Chief Pilot?....


....just be truthful.
Good Luck!