That is a really fantastic question. Unfortunately Photo Engineer is no longer with us, and I don't know if there are any current contributors to this forum who are able to answer the question. I am certainly not qualified to speak on such things, but I'll take a swing at it.
It's my understanding that stabilizers can be used at different points in the process for different purposes (1).
During precipitation, growth and ripening
Some stabilizers adsorb very strongly onto the surfaces, preventing access to the crystal surface. This causes them to be growth restrainers, as you mention (2, 3). But I think that this can sometimes be a desirable effect if used in a controlled fashion. If the stabilizer preferentially adsorbs to a particular crystallographic facet, this can prevent growth in that direction, causing it to be a shape-directing agent. So in addition to controlling shape with vAg, it can also be controlled with shape-directing agents.
Before and during chemical sensitization
Apparently, stabilizers can also be used to control the specific location on the grain where sensitization occurs (4). My guess is that in order to achieve this effect, stabilizers would be added at various points before and during chemical sensitization. I believe that chemical sensitization (aka finishing) is the biggest gap in the knowledge of home emulsion makers wanting to get to high speed. This is a total black box from what I can tell and AFAIK has not been published anywhere in detail. It seems like it's an incredibly complicated process with dozens of steps and precise additions, temperatures, and hold times. Unless some insider comes forward, I think we'll be stuck with trial and error if we want to try and venture beyond ISO ~80. But I'm guessing that stabilizers are involved in some of the steps.
After sensitization
I think stabilizers are also added at the end of the make to prevent fog in the stored, coated material.
Certain stabilizers may also have secondary effects: PMT sharpens the toe and 5-methyl benzotriazole affects the image tone to become more black (5).
So what to make of this? I dunno, but if you are doing a digestion, it seems reasonable to add stabilizer(s) after that step and before chemical sensitization. Before or after washing? I dunno. I would guess that for strongly adsorbed stabilizers, it wouldn't matter that much if you have added the "correct" amount. I suspect that more weakly adsorbed stabilizers might be able to be displaced by the wash somewhat. This is just speculation, I really don't know at this point. My guess is that if you are not overwashing, you may as well add the stabilizer(s) after washing, since I don't think there should be any fog formation occurring during the wash step.
TAI is used at a fairly high amount (0.1 - 5 g per mole Ag) whereas most other organic stabilizers are used at lower concentrations (0.001 - 0.05 g per mole Ag), and the amount is dependent on the surface area (grain size) of the emulsion (6, 7).
I'm very keen to hear any details on the emulsion you're making. I hope this post was helpful and did not contain false or misleading information.
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(1)
https://www.photrio.com/forum/threads/photographic-emulsion-stabliizers.37914/page-2#post-2088673
(2)
https://www.photrio.com/forum/threads/photographic-emulsion-stabliizers.37914/#post-544767
(3) I believe this is discussed in Particle Growth in Suspension proceedings, 1973, SCI monograph #38, but I don't have a copy yet.
(4)
https://www.photrio.com/forum/threads/how-was-tech-pan-emulsion-different.27617/page-2#post-386089
(5) Emulsion Making, Coating and Testing, Ron Mowrey. Pages 34 and 56.
(6)
https://www.photrio.com/forum/threads/photographic-emulsion-stabliizers.37914/#post-544760
(7)
https://www.photrio.com/forum/threa...and-sulfur-gold-treatment.31363/#post-2074735