For homes that are far from the Neighborhood value due to the condition ect...aside from trying to explain to the seller the reasoning behind my ARV and the offer price based on what the neighborhood supports and repairs that need to be done in order to get it to "Appraisal Value" what else might be the best approach. 

The only reason to keep it is further appreciation.   

Should we continue to find another lender or does this seem reasonable?

I'll be sure to provide the denial notice with the reasoning as well as the information that she can request/dispute the report should she wish. 

I was just wondering if when you make an offer like that, do you explain your reason to the seller or seller's agent or just present the number?

Which is obviously good for a number of reasons, anyway (i.e., you need to know your numbers before pulling the trigger).

I just keep going because I like to and see no reason to stop. 

I'd probably let this slide too unless I had a bad feeling about it for some reason.

Being relatively new to this, though, I don't know whether it would actually be a good deal for me (the current owner likely wouldn't accept it either, but I'd potentially be willing to try making an offer if my idea sounds reasonable).

If you get it done, you should thank your lucky stars, and I'm extending every hope that you will.But you probably won't, and you'll be the reason all the gurus have to put up the disclaimer, "ASSUME MOST PEOPLE MAKE NOTHING."