Question about cost basis when selling property with some history.

I hope someone can follow this!

1. A large property on an island was purchased by my great-grandfather a very long time ago.

2. That property was handed down to my grandfather and his brother, jointly.

3. Together, they subdivided the property into multiple lots and dispersed them with Quit Claim Deeds to several parties throughout the family.

4. The lot in question was first given to two of my second cousins.

5. They then quit claimed it (in a trade, I think) to my first cousin and my grandmother who were in a sole survivor situation (not “joint tenants”, just “sole survivor” – presumably because the lot is undeveloped).

6. My grandmother passed away, leaving the property in my cousin's name alone.

7. My cousin quit claimed it to his brother, keeping his own name on it as well so they both owned it.

8. They then quit claimed it to ME (in a trade for an equal, adjacent lot).

Now, I’m selling it and I need to come up with a cost basis.

From what I’ve read about stepped-up basis, it appears that when my grandmother passed away, her HALF of the property would get a stepped up basis of the fair market value at the time of her death. The other half likely has a near zero basis given how long ago the large lot was purchased, and then subdivived.

So, from what I can gather that status carries forward to me now…. Basically the cost basis would be set at ½ basically zero, and the other half at the value of the lot at the time of my grandmothers passing (divided by two, so her half).

Is my assessment of the situation correct or is there more to it that I need to consider?