You have your no pet policy for a reason, stick to your guns.

So far, it seems likely they’ll agree to the new terms and rent and stick around, but they haven’t made a final decision yet (not have we).

I have downloaded all of them to a PC, and copied them to a USB memory stick that I listen to in the car, or on the stereo at home. 

Always stick to your offer.

Or should I just stick with Chase for my banking needs and go through non brick and mortar lenders when refinancing?

Stick to your numbers as they should dictate the deal.

Who would want to pay anything for a 1960 2br/1ba single wide that has been set up on a permanent foundation with stick built walls, roof, addition and a huge hole cut in the side to open up to the addition? 

You will usually be paying a bit of a premium in rate usually 1.00-1.50% in rate premium but the advantage is the original note and deed/mortgage security instrument will be recorded in your LLC's name (no due on sale risk of LLC post closing transfer with a conv/fannie/freddie mortgage).If you want the lowest rates possible then you may want to stick with the agency/conv paper and doing that post closing transfer after you've seasoned the agency note/mtg so that the lender can get a chance to package it up and sell it before you do that title transfer.

My advice is to pick one strategy and stick to it until you excel in it!

Talk to other RE investors that are doing it to determine which of these strategies resonate with you and which one you can afford financially.2) Stick to this one strategy until you excel in it.