You are going through all the right processes Mark - it certainly looks to me as if you are earning success, and you will achieve it. Better still, by now you are pretty familiar with the architecture of that machine, and therefore with Honda OHV self-propelled walk-behind mowers. Every one you work on from now on will be relatively easy.
One of the things you are learning is that hard gum is pretty difficult to get off, and on a modern emissions carburetor it has to be removed to get a good result. FWIW, in my experience so far the GXV140 accumulates more of the stuff than other Honda engines. By the time you know what it takes to get a GXV140 clean, you should be able to handle the others quite easily.
As you said, you should get a uniform line of carb cleaner coming out simultaneously from every one of those holes in the emulsifier. Until you do, you can't expect it to run with the incredible smoothness of a well-tuned GXV140. It's almost eerie - extraordinarily smooth, so quiet that if you mow with the engine idling (which you can in short grass, provided you have 4 sharp blades fitted and you only require a Victa finish, not a Honda finish) you'll find the loudest sound you can hear is the grass hurtling around the scroll to the catcher. At any speed from just above idle, you'll find it takes quite a bit of grass to make any difference at all in the exhaust sound: that engine has rather a lot of torque.
When you get those jet drill bits, aside from being careful not to break them (the tiniest one is the one you use most, and it is only 0.012" diameter) you need to be careful not to leave a trail of inadvertently drilled-out jets and emulsifiers behind you. Until you know the size of the hole, try to avoid rotating the drill bit when you push it through, and where possible, push it through blunt-end first. A brand new HSS drill bit goes through a slightly undersized hole in brass very easily, cutting the brass like butter. With emulsifiers there are normally only one or two sizes of lateral hole. If you get one of them at the top clean, and one of them at the bottom, you can then select the drill bit which fits each of them dead-size, and put it through all of the others of that size, twirling it with the pin vice if necessary. You can then make a note of the sizes, and next time you have that type of Honda carburetor in front of you, you can go straight to the right sized drill bit in the pin vice, and twirl it through all of the holes in no time.
