Well, since I was the one who wrote that, it's probably fitting that I comment on it.
The past 2 shows I've done have been this way, and the next show I'm doing will be this way. It's also happened off and on throughout my career, and was almost always the case when I was non-equity. I should mention that all of the instances recently have been on rather small shows, with casts of 5 and under.
So to answer your questions from my experience:
How do you do it?:
I don't know. It just happens. I will say that when I work for larger organizations where I'm the ASM or the SM with assistants, I find that I have forgotten how NOT stressful this job can be. Really, I find it to be quite nice when I have assistants.
How do you prioritize what really needs to get accomplished?
Well, all of it is really top priority, right? But I suppose there are a few things that can be lower on the list. Line notes has to move down the list. Many times I'll try and keep them caught up during the rehearsal, otherwise I know I'll spend all night with them. Often, when not having any assistance, I'll tell the actors upfront that they'll only receive line notes a few times during the process. It's incredibly hard to take them when you're on book, watching props, etc. etc. Another thing that gets pushed down is the coffee setup. I do what needs to be there. They have coffee and cups and creamer. No frills. If they want something special, I let them know that they're welcome to bring it in.
How do you keep the outside hours of work to a bare minimum, and still get everything done?
I keep my laptop at my table like many people these days, and I'm lucky to have a computer with almost silent keys. So when working on the schedule, I can usually do it directly on the computer. Report notes and prop notes can be the same way (though I admit that I always prefer to get them on paper first---I don't totally trust technology). That's the biggest help for me, having the computer there.
How do you function in rehearsals when there is a book to watch, sound cues to run and props and furniture to attend to?
Very carefully. The actors can see that I'm multi tasking x 10 and are usually forgiving if I'm not right there on book. I pause things for scene shifts if something needs moved in rehearsal, or if it's a big thing, suggest we take a 5 (and I always make it 7 so that I can get to the bathroom and refill my water too!) Basically, I just do my best, knowing that I will make mistakes because I'm human and because too much is being asked of me. If the theatre has problems with any mistakes that are made, I'd simple let them know that I was doing everything I could but that to function at 110% I'll need an assistant. That's never come up however. Theatres know what they're asking you to do.
Who supervises backstage during the performances?
Right now, I'm calling the show from backstage since there's no ASM. Other times, and I've had to request it, the main run crew person is on headset backstage. Only a few times (and in smaller independent theatres) have I been calling the show from out front with NO crew backstage. It's scary and it usually leads to problems, but again, the theatre knows what they're getting into.
I can expand on much of this, but I'm not going to right now. I'd be happy to answer any other questions though if you'd like.