You could get an umbrella policy if you need another layer of protection.

The substitute insurance was $25/mo higher, and we also had to get a different umbrella policy at another $23/mo premium to the existing one.  

Though I guess we can keep the rental property in our own names and then I can raise my umbrella insurance up to $2-$3m to be safe. 

Yeah, I do lean towards you being right, since the deed representing a parcel without regard to its use is really the financial instrument transferred, and whatever happens on the land arguably falls under that umbrella and can't really be separated out.

I've read mixed/conflicting advice on here about whether it's more beneficial to buy each one via LLC or would buying under my own name and supplementing that with a hefty umbrella insurance policy?

Just get an umbrella and call it a day. 

I would consider speaking with a good insurance provider for a strong policy in addition to an umbrella policy.

Account Closed - You honestly probably don't need one and would be fine just getting an umbrella policy if you were worried about protection,  but I am not a lawyer or accountant. 

If it's your first deal and looking for liability protection, get an umbrella policy and move on.

I like umbrella policies for asset protection.