I have landlord policies for my rental properties in TX and AL states, but I am not able to get an umbrella policy form my current insurance company, because I do not have car insurance and primary residence in US, as I am not a resident in US.

(The claim situation)How did the umbrella policy protect you?

If you are worth “something” then you need the umbrella policy.

Also, most Umbrella Policies only pay out if your underlying policy pays out, and the underlying policy will do everything they can to find an exclusion or that you were negligent (which you probably were) in the cause of action to get out of paying the claim.

Quote from @Brandon Larson: It's important to have established policies and procedures, but I wouldn't put a lot of effort into that with only a duplex under management.

That'll help you figure out what direction to aim in before speaking with a bank to figure out how much you can qualify for. 

Loss of rental income is only covered if it is listed in your policy.  

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Get replacement cost hazard insurance along with an umbrella policy of at least $1M, probably double in your area.

Deal flow is tough right now, so I would aim more at 6-12 months to close your first syndication deal.