Okay, so here's the answer to my problem posted above. In case someone has a similar issue in the future.
I posted the same question on AHA forum, and two of the responses helped to solve the dilemma. First and foremost, I didn't know that a refractometer will only give a Original Gravity reading, without needing a conversion, BEFORE any alcohol has been created, in other words, when it's still considered wort during your brew process. AFTER the wort changes to alcohol, after fermentation occurs 4-7 days in, the refractometer reading has to be entered into an online calculator to convert your number into something close to what you're looking for as Final Gravity (
http://seanterrill.com/2012/01/06/refractometer-calculator/ as an example). Evidently this is obvious to many, but I didn't have a clue! And my instructions for the newly purchased refractometer didn't mention it either. So, my 1.035 refractometer reading translates to a Final Gravity around 1.016 on a beer hydrometer. I was in good shape.
Secondly, make sure when you buy a BEER hydrometer that it's not a "Proof and Tralle" hydrometer. The P & T hydrometer that I unknowingly bought, is worthless when used in beer. It's only good for distilled alcohol, those with specific gravities LESS than 1.000.