I'm n00b to this art of shaving, I'm not going to criticize you. For me I just performed short strokes when alternating between each hand. Hopefully that'll work with your left. :Beer:
I'm left handed and I didn't do as good a job shaving since it was my first. It wasn't that I couldn't do it with either hands. The reason being is I didn't want to force something I wasn't really confident in doing so I didn't stroke as much as I should've. The shave wasn't as smooth as it should be but decent enough there wasn't any big blotches or anything it looked more like 5 O' clock shadow. Either that or my hair just grew really fast as I'm not used to seeing it like that on day after shave. It's usually after 2 days. It's strange. I don't know maybe I'm crazy.
Anyway, when it came to neck, I gave myself razor burn because I really got into it :o
I shave my head with clippers using either hand switching the same way I would straight and I get clipper burns as well because I just like massaging back of my head but mostly during summer season it tends to get sticky and I've 10 bulbs in my bathroom and no fan which results in my doing several passes on my scalp but usually get burns on back of my head. But that's my problem :P
This is 10+ years of cutting/shaving my head be it spike style, normal hair, and shaven. I'm just weird like that.