I can do a pretty darned good imitation of several barred owl calls,which they too will often come investigate, but the GH is just too low for my vocal range. I've tried and tried and can't get it. Any tips?
If I had a man's deeper voice it might be easier.
I also have a difficult time with the descending trill on the BO call. I get the downward note just fine but I botch the trill and end up sounding like a sick horse trying to whinny. Best for me to just leave it out.

Try opening throat and calling from the chest. I am female but had to train my voice deeper because in my twenties I sounded like I was 8 on the phone. It took years but I think it was worth it. I can also attract a few of the hawks with whisles but not many. Singing in the car with deep voiced singers helps to train the voice.