A gradual increase may have been a more successful approach.  

We deploy 7 categories of criteria which each have a weighted value.

Also I can understand having debt to family can be weight on the shoulders and stressful.

If you are not paying rent then doing that and carrying your own weight at home will relieve some of their stress. 

So my question to anybody out there is how much weight would a new HVAC have on the appraisal vs a used HVAC? 

The liability is too many "sticks," all the balusters that create a very cluttered look, as well as obstructing half of the lower story windows.So first, let's replace all those sticks with a material that is less visually obtrusive, emulates the architecture, is far more updated and hip, and affordable.https://youtu.be/SPKgdEqnR3QYou could also do a slightly more designed baluster at the second-floor front-facing landings to celebrate those entries and add interest.Wrap approx. the bottom third (or 36" to the railing) of the second-floor posts with 1x to give them more visual weight, and create a very simple capital at the top.At the very base of the stairs (ground level), create two simple but very LARGE newel posts, and if at ALL possible, cap each with a very clean-lined light fixture.

Find out techniques to convince them that even though I don't have some six figure some to bring to the table I'm not just some dead weight trying to leech off them.

A good agent can be worth his weight in gold-pressed latinum.

Do you recommend making the jump to market prices right away or easing it in more gradually? 

Once you excel  in one niche, you can gradually add another.