You can’t use inversement because it means “on the opposite* while in fact, you describe a similar situation.

What you want to state is there is some symmetry, you might then replace inversement by de notre côté aussi:

Parce que, de notre côté aussi, on s’arrache les cheveux pour les accents français !

I wouldn’t use a word that means a strong opposition, because you want to say it’s the same thing with French accents. I would better say:

Parce que, de la même manière, on s’arrache […]

It’s more a parallel, a comparison, than an opposition.

And I couldn’t explain why but the use of “parce que” with “inversement” sounds strange. This sounds better to me:

Et, inversement, on s’arrache […]

Still, I wouldn’t say your sentence is wrong, French people could use it this way.