Have you listened to the Command Zone podcast before? They do a series for each Commander release focused on this very thing -- a budget (around $25) upgrade by changing about 10% of the deck (though they often end up mentioning more than 10 cards to add or remove if you'd like to change it more). Great series. It also analyzes which commander has more synergy and support right out-of-the-box (spoiler: it's not always the face card), and helps focus the deck a bit more on that strategy.
Here's a link to the Kathril deck:
https://youtu.be/9Y5Wms1gMaA Although, if you don't like watching videos or just don't want to watch the whole thing, they put a link to their upgraded decklist in the video's description.