The Reddit info concurs with all the tidbits that I have heard over the years.
What jumps out at me is that there is a fair amount of guessing - which is pretty typical in the world of art.
There is never just one way to do anything - and artists can be secretive when they discover things that work.
Experts can be unwilling to share their trade secrets - so up-and-comers often have to figure things out on their own.
Thankfully, you have a test panel - and hopefully, you will figure out something that works --
my most emphatic suggestion is to be very upfront with the artist that you have never done this before
and you can't really guarantee the outcome.
It is concerning that she might not understand the difficulty of getting anything to stick to gold leaf.
If you spend any amount of time trying to find something that works - but you don't really come up with anything --
what is she going to do? You can't be responsible for the outcome - when she did not research the lettering part of her project until the last minute.
I know this sounds pessimistic -- but it comes from a place where I had learning experiences - taking on jobs using materials for the first time and not having a very good outcome. Through a couple difficult jobs, I learned to educate the client and prepare them for the possibility of Plan B.
Plan B in this case would be to do the lettering on paper, gild around it, and adhere it to the paintings. I'm sure that would not be acceptable to the client - but you can't guarantee ahead of time that you know you can get your lettering to stick. What if you do a beautiful job and then it starts flaking off next year? For your own peace of mind -- I think you need to discuss with the client that you are willing to figure something out -- but you really can't make any guarantee about the longevity.
I have no idea if gouache and egg yolk will mix. My recollection is that the egg yolk is mixed with pure pigments - and possibly other ingredients.
I've used glair and it worked -- but never on a gilded surface.
Metal nib - it might work - if the fluid wants to flow and you don't have to press down very hard. A quill might be perfect -- but, unless you have been cutting quills for a while - you might not have time to learn that. The fluid beading up on the metal is probably going to be the hardest part.
Hopefully - you will figure this out and have a wonderful new technique to offer for future projects. Keep track of how many hours you spend on your research, etc. You might not bill all those hours - but it's good to know. Maybe discuss it with the client.
Sorry for the delayed response, my sons birthday was Friday and it turned into a weekend long celebration. Like I said I was excited to hear your thoughts on the matter and potential foreseen issues to talk with Anne about!

Not pessimistic, more like realistic. It definitely was enlightening, and I felt it gave me a little more confidence to point out the possible pitfalls in this project.
We met this weekend and she is a really lovely and kind lady. She has been doing her own research and realizes the ask is no easy feat. That said there were alot of things she was willing to bend on if needed (like varnishing/treating the gold leaf to if I can't find an ink or paint mixture that will adhere and not immediately crack or flake after drying). She was also very gracious in knowing its very possible they may flake or crack years from now, but it is what it is.
She hasn't gold leafed all the panels and is giving me time to practice & test in case we end up going a much (much) more tedious route. And she is aware that she'd be responsible for that work, I am solely working on the lettering of the project and that's it. I am not an expert in gold leaf so I wouldn't want to be responsible for that.
I do have a gold leaf panel to practice on and I plan on doing a swash test with the inks I already have on hand. And if nothing sticks (pun intended

) I'll branch out from there. I plan on starting with a metal nib and if that looks like its tearing at the leaf then I'll try a brush as you suggested. I know nothing about carving quills and as much as I love trying to new things.. all things in moderation

I'll post an update on how testing goes

Thank you again for the help!
-Aries