A lot of banks will reject you, I just recommend calling as many as you can until you find one that can do it for you.

if they reject it, on to the next deal. 

If I want $100k for a house, and I get 2 offers, one for $100k and another for $95k, unless I think I can significantly expand my upside for minimal downside risk, it would be foolish to reject and say "best and highest".

The tenant cited that I had rejected 25 applicants, and that I am unreasonably obstructing his efforts to make full rent.

I take several and select the most qualified but at most I have had 7-8 and several of the earlier ones had already been rejected.  

They actually analyse your project online and accept it or reject it , they apparently ask for nothing beside estimations of costs.

If they don't give me that info, the application automatically gets rejected for being incomplete application.

Made an intial offer of 95000 but was rejected.

But, you likely need to first give notice of non-renewal; then offer your new agreement and terms with a deadline to accept or reject and vacate that is within local requirements.

I rejected the property based on these findings.