I agree with the comments above that point out that any lender who would do a loan like this (not all will) is likely to charge a higher rate to compensate for the higher risk associated with it being an unsecured loan. 

Thanks for the comment Anthony. 

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Also, the PA Association of Realtors has a standard form for it, and that form includes phrasing that requires the seller to present the offer which triggered the escalation.

the  rental income for  present and  future rental income  can be  counted to a certain degree  ...so this should make your  dti ratio lower ......in most cases  rental properties will   cash flow  positively  or at least  break even   from a lenders  qualifying perspective  ...fyi - lenders  will use  your schedule E  for analyzing rental income  for properties  owned for  more than 1 year

Curious, how did they present the justification for the rent reduction?

There key resources everyone should have before starting such as a real estate agent and attorney.You will not know everything, and each deal can present different challenges.

Pick you agent wisely, because the presentation of the listing and the skill of the agent can easily safe - or cost - you more than the entire commission.

But, anyway thank you all for your comments. 

A Heloc would keep your current loan in tact but also enable you to pull the trigger should a deal present itself.