Sounds like an unreasonable seller and the most likely reason for them not wanting an offer with a financing contingency is the property is in too rough shape to get financing on it (structural damage, fire damage, etc.) or won’t appraise anywhere near asking price.   

What I am seeing is older residential units being purchased, eventually torn down and upscale apartments replacing them.

From the sounds of it, I won't be making that mistake.  

Definitely what I was thinking and sounds like it can be done. 5.25-% rate on a 1.2$ house is definitely more appealing and opens doors up as opposed to 6.7+ rates.  

As @Nicholas L. said, it sounds like you are doing a BRRRR.

Personally I only use my HELOC on short term projects like flips, new builds and BRRRRs where I know I will be replacing the capital within months.You may be better off waiting a year and save up more cash or liquidate your index funds if the returns on a property will be better.

Good luck—it sounds like a great opportunity!

It sounds like mistakes were made on the properties but I'm also questioning the market (you didn't say where these are). 

@Matthew Paul sounds like a newer agent that you're dealing with here.

@Howard Cheng, Qualified and non-qualified use only applies to the period of time you owned your replacement property (the converted property).