I've never run pbp either, so I'm no hope to you there. However (like our very own Sigulf) I run 1 player - 1 GM games for my wife, as well as her running the same style of games for me. This is sort of in the ballpark of the second point you are asking about.

I've had players move away, stop playing rpgs, and also die - and frankly I don't have the energy to find players for a new group and playing online doesn't appeal to me at all. Thankfully BoL engine games work perfectly with 1 Player- 1 GM. And as games run with BoL mechanics are by nature pulpy, this style of play fits the original source material perfectly.

Here's an example of what we do, about one of our games: 
Hollywood Pulse is an episodic campaign set in 1930s LA, featuring my wife Alison's PC, Judy Katz - a Hollywood gossip columnist (her column is called 'Hollywood Pulse'); and her husband, my PC, Tom Spencer - a private investigator. Alison runs games for Tom and I run games for Judy - both of whom keep coming across occult and supernatural threats in Tinsel Town and the surrounding area.

When it's a Tom game, Judy appears as an NPC, when it's a Judy game it's the other way round. Sometimes the other PC is hardly in it at all. Sometimes they are more part of the game. When that's the case they let the 'Player PC' make the running with how the investigation develops and rarely make any suggestions re: clues, etc. Essentially the GM runs their PC in full NPC mode.

Sometimes the 'GM Character' is what I call an 'Allied NPC', rather than a full PC like Tom is. This is when the game is something only Alison or I run exclusively. An 'Allied NPC' is generated exactly like a PC, but has no Hero Points and rarely has any advancement. These are rather like the best buddy of the protagonist in a pulp story - more competent than a regular NPC but less than the major villain or the protagonist.

In some of our Sword & Sorcery games, like our Hyborian campaign, Alison's PC Aja, has three 'Allied NPCs' to call on - but then Hyboria is a lot more dangerous than 1930s LA, even when it features vampires.

I think something along the lines we do these days might work for a GM-less pbp game with some tweaking, possibly with some sort of GM simulator/set of questions aid? Perhaps people with more experience of pbp or online gaming may be able to offer more focussed help. 

I tried pbp for the first time during the pandemic but it wasn't for me.   We were playing Star Trek Adventures and basically a conversation that could have taken 10-15 minutes (no actual real plot advancement but just rather introductory character interactions) in person took three weeks online with pbp.   We didn't have a particularly strong GM to advance the plot as he wanted to let things progress organically but I just ended up bowing out at the end of the month as a result.   I hope things turn out better for you though and it's definitely a gameplay style that works for many others.

It could definitely work but you'd probably have to curtail/put a hard limit on the back and forth conversation to NOT imitate a real life back and forth unfortuantely especially if folks are only posted daily as opposed to updating multiple times per day.  That's were we ran into trouble as asking a simple question took roughly 1-2 days to ask and answer with most of the group.   And if that answer led to a followup question then it was another 1-2 days.. and so on...

I am sorry for being off the boards for some time, and I don’t have a lot of time to write, but this is in my wheelhouse. I have played pbp since at least 2008, and I play solo using Mythic (which pairs greatly with BoL) along with other tools. I have done a few collaborative efforts of GM-less games using Mythic and other tools, and can say it can work. The sword and sorcery “buddy” shtick and short story format can be conducive for a duet sans GM endeavor. BoL being very mechanically basic can further facilitate this.

It can be difficult without a GM filling a “chairman” role to push things along and keep a group well-directed. Pbp’s tend to fizzle out, so that’s an added risk. Knowing the risks is useful, but shouldn’t deter you.

I would be willing to try something if you are willing.