The title person contacted me before the banks closed, to let me know they don't accept cashier's checks for more than $50k.

Strong screening process with solid qualifications will allow for a landlord to find another reason to not accept them.  

So rent might go up 2% to 3% a year but they want to pay a rent bump of 6% in 3 years etc.National tenants there is generally less risk in accepting these terms as they are likely to still be around and you see the increases.

I absolutely do not accept any evictions, and the renter has to make 3x the rent for me to be comfortable...

Not sure what the bank would accept for the house.  

If I shop around to other banks, is it possible that I can find one that will accept me?

The accepted standard for determining current market price is to survey the market area with considerations for quantity and quality for a "going price" of the goods and services in question.In a widely cited case, the FTC went after a Baltimore roofing contractor in the early 1970s successfully alleging the contractor was overcharging consumers to reroof their homes.

In order to rent out a home in the City of Detroit you need a C of A (Certificate of Acceptance) and a C of O (Certificate of Occupancy) therefore you can't collect rent. 

It seems to me, he use to advocate tied performance and rent credits - though not to the degree of many (there are a couple of websites out there advertising "passive" Rent-to-Own: you put up the money, they find the property and lessee / buyer - where the agreements appear to be tied.We do not have the equivalent of Dodd-Frank and the Safe Act here ... yet ... but do not be surprised if we follow the lead.  

I am studying towards degrees in Finance and Managerial Economics.