Custom kitchen & bath remodeling, interior/exterior painting, full interior gut jobs to include removing walls and installing headers. 

Are we in the ninth inning or the 5th inning of a double header?

Unless I'm reading the it wrong, it sounds like these would be the appropriate code sections for the beam/girders and that in terms of sizing the engineer is correct.https://codes.iccsafe.org/public/document/IRC2015/...R404.1.9.2 - Masonry piers supporting floor girdersR602.7(1) - Girder Spans and Header Spans for Exterior Bearing WallsR602.7(2) - Girder Spans and Header Spans for Interior Bearing Walls

(I have no vested interest- just mentioning my perspective) This is what my header looks like on USBank currently. 

But even in the second case you mention, if a permit is required you should get one - doors, walls and windows require headers, right?

I might know the homeowner ;)  Fortunately, the drywallers c. 1950 "coped" the drywall around the original oak header/capitol over the door in the wall they built to divide. 

210- 235 depending on pitch, includes all. avg roof 25- 30 sq, Take down a wall and install a header, ( GC scare the  homeowner ) 5k, WHAT!!!

Specifically, start reading from the header that says "Verification of Multi-Unit Property Securing the VA loan."

Toe nail 2x4 into header and new bottom plate.  

I can only assume that all of your door and window headers will now be undersized.