Inspired by this post I've managed to implement the requested feature in my program Mtgdb.Gui, it's free and opensource.
The screenshot below shows the list of decks filtered by a condition that you own 90% or more from the Main deck.
So basically to search decks based on the list of cards you have you need to
Step 1. Import your collection to Mtgdb.Gui, which is going to be easy considering you already have a text file with your collection.
Step 2a. Sort the list of decks by percent of cards from Main deck you own in descending order, by clicking the corresponding field.
Step 2b. Alterternatively as in the screenshot above, you can filter the list of decks by using search input.