Since Desjardins bought state farm its really a desjardins policy right?

I think ANTHONY Robbins would say no referral no safety net but you have a family.

If this company does not offer higher limits you should consider an Umbrella policy  That policy will provide an additional layer of Liability above your homeowners Liability and your Auto Liability.  

In addition, they are also pushing a "first come first served" policy which requires that landlords grant occupancy to the first qualified applicant.

I can tell you from first hand experience that what you state has been true for me (unfortunately, I am one of those learning the hard way).I think, if possible, one should question what the first-time CHA inspection pass rate is for a particular PM, % of units that are under abatement, policies and abilities to collect the tenant portion of rents, costs of an annual inspection (from what I've learned, there are always costs after each inspection), plus what vendors they use for things like exterminators. 

Does anyone have advice on whether I should keep my policy or switch to a landlord insurance policy?

However, my brother in law is with Liberty Mutual and recently told me that they'll now write standard landlord or homeowner policies on residential property held in an LLC.

They are only checking to make sure the items in the house work and that there are no safety issues.

@Lidia Syrwid sounds like you need a builders risk policy. 

Again check the policies and make sure you are covered for scenarios you can come up with.