I've read about Heloc's, cash out refinance etc. but don't have a firm grasp on the minutia of how these work and what the best plan of attack is for funding rehab.Second: Although I'm preapproved, is there a concern for my lender rejecting the deal because of the rehab involved or the lack of a Cert of Occupancy at closing? 

Spend the money and get matching paint, don't cheap out and buy whatever paint rejects the local hardware store has.

You can explain why your top price is what it is, and give them an offer of $63k, which they will almost certainly reject.  

The worst that can happen is they reject your offer.

I applied for a HELOC with TD Bank, and after nearly a week of calling & checking on my application (they initially claimed it would take only two days), they finally said my application was denied. "Based on what...

Good morning-Working on multiple things...1-property was submitted for offer and seller rejected. 1st stages on market not long enough for seller to realize the list is too high given the condition and comps. seller thinks they can get what is listed or close to.

Please, reject her application and tell her to move to New Hampshire.  

I've also read about buyers making low offers every 30-60 days and having this offer accepted after being rejected several times.This 85% rule suggests your expenses will be 15% of your gross rental income.

What is a nice way to inform this tenant of my reason for rejecting her.

You will get a bunch of rejection scrubbing the leads but if you have the drive you might make something of it.Be very careful and read ALL the documents in writing and have your attorney review.