Hi! Lost & Astray is a very interesting ruleset. I appreciate the attempt to be explicit about PbtA moves and expectations. Codifying various dungeon delve bits into Discovery, Navigation, Peril, and Progress scores appears to work to support generation of this specific type of adventure. Clearly categorizing the moves according to the types of actions in the delve is also very helpful. 

Admittedly, I am unlikely to play the ruleset but will borrow concepts and mechanics for my home game. Keeping track of the various modifiers and subsystems and if/then conditional outcomes is a bit more bookkeeping than my table prefers. 

Shared refereeing as written in this game is something I’m very interested in. However, it appears that the Ref falls only to the Leader until such time as another PC escapes or dies. So if they all survive and exit as a party, the Leader is the only Ref…

Do you have experience or suggestions for multiple Refs in less lethal games? Have you thought of a mechanic to share the role across the other players?

I see.

That bit has not changed, but what follows should be a bit clearer...

This links back to the general Speaking Order rules. Basically instead of the Ref being the only one doing the Ref job... the Ref is the one with precedence, but then everyone else can have a chance to pitch in ideas and answers. The same happens in the Ref Phase, where the system basically asks questions to the players.

Thus, the Ref job is not a monolithic thing that needs to be passed around. Anyone can join in any time they feel like.

As mentioned somewhere else, having clearly defined roles is mostly for order and clarity. The group always knows WHO is supposed to say WHAT and WHEN. Once that is clear, they can easily behave in a more relaxed way, offering ideas at any time, if/when they feel like. Some groups benefit (or ever require) a more hierarchical order to feel at ease with the game. Some players have problems with (or categorically refuse to) engage with Ref-side activities while they are still also playing as Delvers. For them this structure is beneficial.

For others (maybe your group?) it's more like a vague guideline to follow by feeling ;-)
In the case of this specific game element, as long as your group feels good with it, it's all good. The important bit is avoiding that same person asking a question and offering the answer too. That is usually quite boring and shifts the experience too much towards "shared storytelling" rather than an actual game where you get challenged and surprised. 

I was also thinking... what kind of game are you trying to put together?

If team-driven action and dungeon-mapping are not the core of your ideal experience, maybe a very different solution might work too?

FateLess is more focused on campaigns over one-shots, and individuals over teams.

Touched by Evil and Ikigai both focus on a single protagonist shared by the group of players.

Cerin is a lighweight (and lighthearted) game in between these extremes: team focused, one-shot, and less procedurally strict than L&A.

Then outside the realm of my games there is a vast variety of awesome titles that offer all kinds of gmLess solutions :)
What are you looking for exactly?