Non-Jewish Jewish Marriage

Hi,
This question is targeted specifically at Israel.

I’m Jewish, I was raised in a traditional household with celebration and participation of all holidays, I’m a 21 year old male.
The one and only person I wish to live with, is 20 years of age, and we’ve been together since she was 14.
She has a Jewish father, a Jewish grandfather (from her Mother’s side) but a non-Jewish grandmother. About a thousand years ago she would still be considered Jewish, but the latest Jewish Law only identifies a mother-Jewish connection.
Don’t get me wrong, she grew up with Jewish holidays just like I did, not as traditional, but she still did, she speaks fluent Hebrew, learnt the Hebrew Tanach in an Israeli school, etc.
However, as we were planning our wedding, we found out that we cannot preform a Jewish ceremony inside Israel.
Not a reform one either.
She has no religion based on Israel’s Interior Office decision.

My question is very simple, is anyone aware of what can be done inside Israeli to allow us to go through a regular marriage? It DOES NOT have to be through Rabbanut, just a very simple Jewish ceremony.
Our family members will not travel to a foreign country to attend our marriage. This is absurd.
Hopefully you can understand. And no, she does not wish to go through a conversion.