Transferring ownership of a deposit the day after eviction is not a "normal" occurrence, and is certainly not normal when the same lawyer does this 80 times per year. 

., When you do a 1031 exchange the basis of the old property is transferred to the new property. 

She might have to purchase in her name and then transfer ownership to the LLC afterwards.

Has anyone come across any issues with insurance being enforceable if they transfer over a property from a personal name to LLC with a loan on it?

Assuming your current loan is a conventional loan, you can transfer into your LLC without refinancing.

Would it be a good idea to transfer these rentals to an LLC in order to qualify?

Your agent should be able to assist with this, but typically you need estoppel agreements to transfer the lease from the existing owner to yourself. 

@Jeremi Ramos do an addendum to your PMA that has all the Portfolios and Buildings on it.Be sure to include language though, that allows you to auto-transfer funds between the Portfolios/LLCs to cover your management expenses.Otherwise an owner could screw you on fees by letting portfolios go negative on their balances.

Is this as simple as going to to county recorder and transferring it into my name?

Most attorneys in California advise against them as they cost about $800/year, and you also have to transfer a property into your personal name before a sale, so they do not help with anonymity.