Perhaps that carrier really doesn't want the business/exposure, but would gladly take it for an extreme premium??? 

Unfortunately, if their carrier were to deny helping you, the burden to prove the tenant's negligence would be up to you to prove (likely in court/mediation).  

Our carrier charges an extra $10 a month for this.  

A lot of carriers have stopped accepting Landlord business in this hard market.

I have heard this from several of the insurance carrier executives.This increased cost forces the carriers to take large increase or exit the market. 

Can anyone recommend a insurance carrier or agent that I should contact to try to find lower rates?

Your carrier is probably rejecting coverage, because you have a conventional policy that requires a RC coverage amount, of which you are drastically below that. 

@Matt Wells we are seeing rates with all of our insurance carriers go up 10%-15% on renewals and new business. 

(profitability issues within carriers, we are not drilling for oil as much and oil goes into EVERYTHING in a house so the costs are higher, and for some reason people across the US are filing more petty claims most likely due to the economic issues and majority of people do not have cash on hand for medium sized claims etc.) 

Find out what the market is and how your current carrier rates compare.