I use hot water for creating my lather. Never an issue with drying out. Mug and brush soak in hot water for a few minutes while I'm grabbing the razor and soap. I do soak my badgers, boars and synthetics, fully aware that badger and synthetic don't need the soak like boar does, but I like a hot brush and a hot mug from hot water to create a nice warm lather. But that's me. Ask all the scuttle users about warm lather.
I suspect hot water doesn't really effect veg based soaps all that much. For myself, I always use piping hot water for my lathers. If it does start to dry out, I can always add water. ...and yes, that recommendation came from that 80+ years old book. Soap making has come a long way since then, and for the barber, time spent walking back and forth to add water to the lather equalled money not being made. You got to take those old time recommendations with a grain of salt sometimes. Edit: the lather forming peaks as a way to judge a correct lather is a modern thing, a theory formulated by expert latherers. It's not the only way to gauge a correct lather, but it's simple, easy, and mostly foolproof.
Forgot to mention. The old scuttles with the water reservoir for the brush and the soap on top are relics of a time when there was no hot water on tap in most American homes. You heated the kettle on the wood fired stove, poured the boiling water into your scuttle and made your way to the water closet or wherever else you kept your shaving mirror. You shaved with a straight razor, wiped the lather off with a towel, and did the same for your face. Always remember to put the tools and how they were used in the proper context of the time they were used in.
I fought it for a long time too, Steve. Sometimes you just have to accept that new terminology has become accepted practice, even if it's a terrible description of what is occuring, and the guy that originally coined the phrase has a shaky grasp of the English language. What makes it even more irritating, is that 'bloom' was already a word in use within the hobby for years to describe the 'flower style' blooming effect of a damp brush post shave.
At that point in your picture, I would kiss the water with the top of my brush, and go back in for another minute. It's hard to describe, but I'll try. The lather will have a sheen to it, you only get that off a smooth(ish) surface. And you only get that when most of the micro bubbles have vanished. 80% of it should look like the surface of melting ice cream. Smooth and shiny. You'll see micro bubbles, but they will be scattered about. No more than 3-4 in a cluster. lgnore big bubbles at this point. That is my impression of a good lather. And it will form peaks if you pull it apart, with smoothly defined edges from the motion of the brush. It's a dozen almost imperceptible things, we just know at almost a gestalt level. Once it has reached that point, you can add a little water (kiss the water once or twice) and continue working the lather to thin it down without it falling apart, or leave it thick, as is. One lather gives slickness, the other gives cushion. Both shave well. Dialing in the perfect balance of cushion and slickness? Ahh... That is where doing it daily is the only way to get there. You are perfecting it for your face, and your favorite style of lather. ...and your razor. I know it sounds kinda mystical, but it's easy enough to eyeball it and see where it is at. The mystical part is when you can sense that point from the feel of your brush against the bowl, or if you face lather, against your face. Think of it as a "tell" or that rare moment in a samurai's duel, when the blades are held in position, and you identify the opponent's move in the heartbeat between their moment of decision, and their moment of action. Almost imperceptible, but noticable to the trained fingers. As any tradesman knows, it's not the first 95% of the job that is hard to learn. It's that last 5% that separates the two groups of percentages. Any idiot can learn to weld. It's knowing how to weld for different steel types and thicknesses, which welds to put in first, and the ratio of weld size to strength, how much weld is required, how much heat has been dumped into the steel, and a dozen other things. Knowing how to read a blueprint and a tape measure helps. Depth of knowledge in the craft is the only way to master it. Shaving is no different than any other daily task. Do it enough times, and you'll get pretty good at it, you have the rest of your life to learn.
I don't worry about shave time. I take however long it takes and enjoy it. It's my spa time. Time to pray, ponder, meditate on scripture, or even just digging the tunes on my Pandora stations. If don't have the time to enjoy my shave my way, I don't shave. So what if the puck dries out? It won't hurt it and it won't diminish the performance. If you're using it every day, no need to cover. I keep my soaps in a ziplock bag only because with all the soaps in my rotation, I can stack them. In fact, I use my soaps in the morning and let them dry before sealing up the bag that evening. It also keeps the dust out between uses.
You can add glycerin to the lather, it will add some slickness. I wouldn't go overboard with it. A drop or two will go a long way.