Being left-handed or right-handed, the cutting problems you are having are very much the same. If I were cutting this project, I would put the cutting mat on a table that I can walk around, and I would walk and forth from side to side to get it all cut.
I know it is more work, and there is a time when you can turn the mat without messing up the strips, but it is one way to get the job done.
I have been using a rotary cutter for more than fifteen years and have never wanted to try cutting across the ruler and my arm ... contortionist is just not how I am wired <g> ...
ANOTHER Idea :idea: :idea: :idea:
How about taking a second ruler, using your primary to get that angle, then butt the second ruler up against your stationed first ruler ... remove the first ruler and cut along the right side of your second ruler.
Bring the first ruler back and use it as normal ...
Is that practical? <wave>