With Property you know the limit of risk you are taking, but with Liability claims, you never know, so best to keep that with the carriers. 

Anyone have experience with agencies other than ALE or going direct to insurance carriers for this kind of tenant? 

For the not-so-big-one like you say, I'm guessing most of the damage will be on me, not the carrier.

Current carrier and when it expires  (may want to get them a copy of the current to match limits or to compare limit to what they suggest)

The best source for commercial policies is an Independent Agent (they represent multiple carriers). 

Most carriers are pushing for at least a $2,500 deductible in the current market, and more are even pushing $5k. 

Our regular insurer, State Farm, does not do such coverage anymore, and after checking with several well-known national carriers, I found only one that offered it, but the lead agent couldn't be bothered to put the details in writing in an email.There must be companies that specialize in this kind of coverage, I figure, and there must be other property owners in a similar situation who have such insurance. 

Take the time to understand each line of your coverage and challenge your carrier if you don't need certain items covered.

Contact your title insurance carrier to fix it. 

The brokerages and the errors and omissions insurance carriers are making creative financing more and more difficult for the agents themselves.