So, I know that the title may be a little misleading, but that's the best I could figure out what to put.

What I'm trying to figure out is if it is possible to use this site, or any other site (as long as I can export my collection to it) to tell me what deck I can build from what I have, and what I'm missing based on what I already have, rather than having to click on each deck, and seeing how much it would cost me to get the cards I'm missing for that deck.

The only website that I know of that does that sort of thing is ShoeboxMTG. However, it will only find you decks from "Top" lists from events (up to Top 64). If you're looking for something that matches your inventory to a database of user-submitted decks (because you're wanting to find fun, casual decks, not necessarily top-tier decks), then I don't know of any site that offers that feature. That would honestly be great!

Note that Shoebox offers an "import your Deckbox" feature, that allows you to enter a Deckbox username to grab the list of cards in the associated inventory. It doesn't work with private inventories, obviously.