Unfortunately, character progression in Myth is tied directly to Story completion. That meant I needed a house rule to allow characters to advance via Free-Questing at about the same rate that they would if you only played Stories. Here's the simplest version I could think up, along with an addendum and a clarification that came up when people asked me questions on how that rule worked.
Basically Rule #1 and it's addendum just treat every 3rd Session as if it were automatically the completion of a Story. You don't get an automatic Title each time, but your Item Limit is treated as if you had 1 more actual Title than you technically do so you're not screwed for not starting with an official Story. It's roughly balanced vs the original Story mode requirements and rewards. It's slightly in the player's favor, since some of the Story Acts can run unexpectedly long, but the difference/benefits should be almost entirely about convenience, not power level.House Rule #1: At the end of every third session, the players receive a Deck Manipulation reward. When this happens, items are reset to their starting (brown) equipment for each character, but you can save 1 item + 1 per earned Title. Serendipity and gold are reset to zero at this time as well.
Addendum to House Rule #1: If the Heroes ended the third session while still in the middle of a Quest Chain, they may choose to delay the Deck Manipulation and item reset until the end of the session in which they complete that chain. Further Deck Manipulation rewards do NOT accumulate while you are delaying one.
House Rule #2: When you complete a chain Quest that directs you to add a new chain to the Quest Deck, you may choose to either place that card on top of the deck, or to shuffle it into the deck. If the last Quest of a session tells you to add a new chain to the Quest deck, you may make the decision at the start of the next session.
House Rule #2 is possibly how the rulebook intended quest chains to work, but it's hard to say for certain as page 11 is short on detail and at best kinda lazily implies that's how "pursuing a quest chain" in Free-Questing mode works.
Armed with those rules, I set about cutting the Story Quests apart into their component pieces, fixing and clarifying the rough parts, ditching a few rare truly broken parts, and putting everything worth saving onto Chapter Quest Chains. Provided you occasionally drop in a Tile with Traps rather than simply rushing every possible Quest opportunity, it should be only a very minor impact on play balance, and you'll get to enjoy all the best parts of both Free-Questing and Story Mode.
EDIT: I was asked some questions about how you're intended to use these cards. The person asking was worried that this somehow made the story chapters happen out of order. That's not the case at all.
Put the first card (and only the first) of each chain into your Quest Deck and shuffle.
When you eventually draw and complete that quest, the card it unlocks can either be shuffled into your deck, or can be placed directly on top of your deck so that it's guaranteed to be the next Chapter Quest you encounter.
I don't think of that as a house rule. I'm pretty sure it is what the designers of the game meant when they said in the rules:
"If the players chose to, they can simply game the entirety of a Chapter Quest chain and forego accomplishing any Act or Story Quests. Even if those quests have already been drawn, players can choose to pursue a Chapter Quest chain instead." - Myth rulebook, page 11.
Here's my initial "proof of concept" version, which converts Story #3: "The Mad King". There's a tiny bit of new content on the cards below, but for the most part it is all just text taken from the rulebook's Story section, ported onto Chapter Quest card format. Copyright on all of this belongs to Mercs/MegaCon. I don't think they'd complain about me posting it here, as you'd need the core game to make use of any of this, and the essence of these quests can all be found in the core game rulebook.
The first three Chapter Quests are just adaptations of the "Circle The Wagons" Act from the Story. I converted it into 3 cards, and made the third one optional, so players can choose whatever length and difficulty they want for overall "story".
Failure is unlikely on most of these Quests, as it is in the original. Just in case, I included new penalties for failure in case the Heroes have a streak of bad luck and decide they need to Abandon the Tile/Quest. This "ups the ante" just a bit, and ensures the new format isn't significantly easier than the original Story Mode version.
Also, adding both cards to the deck means you can revisit just the wagon mechanics in later sessions without having to restart the entire Quest Chain.
About 3 Trap tiles to every 5 Quest tiles is roughly the ratio used in the original Story format (for most of the stories, anyway).
The rewards include a Deck Manipulation, because I converted this before I'd settled on the House Rule (see top of page) that makes it redundant. Most people will choose the Title anyway.
There's also some Serendipity bonus on the final card because I don't want to assume the players will call it quits for the day after doing this card. The whole point of doing these as Chapter Quests was to give players more control over the game (including length) and not be straight-jacketed by the Story structure if they'd prefer to be flexible about it.