Make a few polys that leave holes to fill then in the border select tool "cap" the holes and create some edges where necessary

^^^
I do this.
Create faces and insert vertices gives you a lot of control though. It's nice.

I would personally just use the bridge tool in edge mode, but quite frankly you have way too many vertices there than needed. Any particular reason why?

Create.

Bridge.

Cap.

All do more or less the same thing.

But I would get rid of the atrocious amount of useless verts you have first.

Compound objects > boolean

Is commonly used to cut shapes into objects. And it also creates alot of junk geo.