Seems like everyone answered everything for you.My little advice is if you go with the Parent LLC and multiple Child LLCs, please consult with an insurance agent that can put it under an Umbrella Policy so you won't worried about getting sued and reaching up to the Parent LLC.

Do most insurance companies provide landlord property/liability insurance and umbrella policies for properties owned by an LLC?  

What Greg said.If you have a net worth over $500k get an umbrella policy, if you don’t, don’t worry about it. 

In the end I've beefed up an umbrella policy I have, but my question is whether this is a common problem people have when putting rental properties into LLC's? 

Yes there is also different amount of coverage as well as a whole additional umbrella polity you could purchase but that's another subject.

My vision of sipping umbrella drinks by the beach had turned into a nightmare of financial ruin.

Most will charge a reasonable annual fee, but think of it as insurance.Lastly, consider just getting more insurance, typically an umbrella policy to cover your entire portfolio, instead of OR in addition to an LLC.Of course, discuss all this with an attorney!

Shirley: I use Insight Rick Management for my portfolio umbrella policy. 

My original plan was to transfer to a property owning LLC (by quit claim) which will be owned by an umbrella LLC (for anonymity and asset protection). 

If you're worried about liability for the rental, you could always look into an umbrella policy with your insurance company.