What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

I've included an example below to help illustrate this.So different lenders have different rates (which do vary even for DSCR loans) but these are factors they all consider.See example below:DSCR < 1Principal + Interest = $1,700Taxes = $350, Insurance = $100, Association Dues = $50Total PITIA = $2200Rent = $2000DSCR = Rent/PITIA = 2000/2200 = 0.91Since the DSCR is 0.91, we know the expenses are greater than the income of the property.DSCR >1Principal + Interest = $1,500Taxes = $250, Insurance = $100, Association Dues = $25Total PITIA = $1875 Rent = $2300DSCR = Rent/PITIA = 2300/1875 = 1.23DSCR lenders generally let you vest either individually or as an LLC.

So the mortgage listed individual partners (SSN) as the borrowers.

The landlord is "allowing us" to break lease (and handle all the rental ads and showings, of course) but has jacked the rent from $2250 up to $2500.

Additionally, there may be limitations on rent increases and lease terms when renting to CMHA tenants.Ultimately, the decision to rent to CMHA tenants depends on your individual preferences, risk tolerance, and investment goals.

We are considering taking out the required cash to make up that total from our savings, brokerage, and 2x TSP loans from our individual accounts.

@Jeff Miller$40k in equity most banks will not allow that to be pulled, as they have strict loan to value requirements.Whether you put properties in or out of a LLC, does not matter who owns it, but if you are seeking to get bank financing for acquisition they will want 25% down.

I heard that conventional loan would not allow the intermediary taking the title. 

Because both of those are affected by different metrics which you need to essentially measure each one individually before you can really come up with a good decision. 

Again, this is possible only if I am allowed to ask the tenant to move out.I would really appreciate any input on this.