I'm right handed and left eye dominate, had to learn to shoot left handed because I could never kill a rabbit with a 12 ga wingmaster when I was a teenager.
I too, always used right handed bolt action rifles left handed up into my 30's.
Got my first LH bolt action in early 30's (wife got me a LH rem 700 vss 300RUM). That factory rifle is a tack driver btw.
I too didn't think going from right handed rifles to a left handed rifle would be that big of a deal. As I have gotten older and continue to learn and tweak my gear list and shooting techniques over the years, I've found that it does make a difference, I do prefer the LH actions.
Setting up for shots correctly is critical for being able to spot your hits and to be able to make quick follow up shots if needed, especially when hunting by yourself.
I can make those follow up shots, if and when needed, much easier with a left handed action.
With everything else in life, the more you practice or work in your profession the better you get at it. One of my goals in life is to learn something everyday, and I'm teaching my children that as well. Be willing to listen to other peoples opinions/techniques/gear suggestions etc. Take what you like, apply it/or tweak our own gear list if it helps to make us better at what we do.
This is a tremendous site, where we all get exposed to a wealth of knowledge about this great sport.
Have fun out there, Hunting Season is just around the corner!