The solution is simpler than you think; you simply need to add ZERO WIDTH SPACE unicode char between / and " (beginning) and " and / (end).

The default way to do it is

C-x 8 RET zero width space RET 

or

C-x 8 RET 200b RET

But I need to use this priceless unicode char to escape stuff like this in org-mode and so I have bound "0" in "C-x 8" map to insert this char.
Here is how I do it in my init: https://github.com/kaushalmodi/.emacs.d/blob/f3c44e933f45dfdb760540e9f86acc91b55ab94a/setup-files/setup-editing.el#L637
Thus I simply need to do C-x 8 0 to insert the ZERO WIDTH SPACE.

To elaborate more, <0> below is where you insert the 200b unicode characters:

I would like to see /<0>"these surrounding quotes in italics"<0>/.



On Wed, Jun 17, 2015 at 10:46 PM Steven Arntson <steven@stevenarntson.com> wrote:
I am not helpful here, but would simply like to add that I would also
love an answer to this, as well as times when italics don't seem to work
around periods and commas, like "and /then,/ well, ..." (which does not
italicize for me on emacs 24.5.1, org 8.2.1).

Myles English <mylesenglish@gmail.com> writes:

> Hello,
>
> Can anyone tell me what to set org-emphasis-regexp-components to in
> order to allow italic quote marks?
>
> i.e. /"like this"/
>
> I don't understand the documentation and am just not in the mood to
> spend the next hour or so working it out.  (That is a rule of thumb for
> me; if it involves a regular expression, it will take at least an hour,
> and three cups of tea.)
>
> Thanks,
> Myles