I also have monovison lenses.
Right eye dominant, but with reading(close focus) lens in my left eye and and long distance focus in my right eye. Right handed.
With the first prescription I had the same problem of not being able to get any level of focus on the front sight of my handgun, nor the rear blade sight on rifle. My target was in sharp focus.
To compensate, I ended up tilting my head over to the right and using my left eye for shooting my handgun - no work-around on the rifle though
I ended up discussing it with my fire-arm friendly optometrist and he adjust my long distance lens, bringing it back to an 'intermediate' distance and since then all is A-OK on the handgun side, although I am giving up slightly on very clear long distance sight.
On my rifles, I have come to the conclusion that age has won and open sights are not what they used to be for me. Now I have glass on all my rifles.
Back-up iron sights with rear peep sight on AR type rifles are GTG as is though.