I read over a sample personal umbrella insurance policy and it says that they dont cover injury due to business property, and that business property is defined as residential property rented, or held for rental, to others.

Don't assume that it is.If a liability claim ever arises against you for injury or death on your property - and it DOES happen - your risk management will be intensely scrutinized by a plaintiff attorney and potentially a judge or jury.

I have questions into them on whether they would cover it if the commercial policy denies it.Here's the exact language of the exclusion - "This insurance does not apply to animals "bodily injury" or "property damage" arising out of the ownership, use, loading or unloading, handling, or demonstration of domestic or wild animals, including but not limited to dogs. 

My time as a personal banker has provided me with the opportunity to meet a lot of people who are neck deep in 20% APR debt and CANNOT get out of it!!!

You don't want to add insult to injury by offering to buy their house off the bat including offering to do a Subto. 

It protects PM  from both individual and business’ claims of bodily injury, medical costs, and damage to property.

Then to add insult to injury, you get hit with multiple large CAPEX items at the same time.  

I sustained back injury on the job.

They set minimums for coverages, knowing they will rarely exceed those minimums.Lawsuits for injury are rare.

Especially since the city will likely be breathing down your neck