I adore flap bags with sliding chain straps! I have a vintage Chanel jumbo, YSL LouLou, and
Gucci Marmont, though I suspect all those would be too branded for your tastes. I also have two
Coach Parkers - one has the "C" clasp which again, may be too branded, but the other has a tea rose clasp which I adore for its dainty femininity and also makes it far less branded. All that being said though, I actually thought of Massaccessi as a possibility for you when I read your post.
I just ordered a Massaccessi Astra Satchel with a sliding chain strap instead of a top handle, which makes it a double-chain shoulder/crossbody bag. You can heck out the Massaccessi handbags thread here to learn more. The thread is a good intro to the work of MM in general, but if you search the thread for "Astra", you should be able to find photos of the Astra satchel with a sliding chain strap.
Massaccessi is awesome because you can really customize a bag to suit your needs. Admittedly, it can feel a bit overwhelming at first, but everyone on the Masseccessi thread is happy to help, and customizing a bag to suit your needs is awesome. I mean, I really love my YSL LouLou and Coach Parkers, but I hate the middle zip divider in them. With Massaccessi, you can remove features like this if you want (or add them in if you want). You can choose the leather, lining, hardware color, and you can also ask for certain add ons or remove feature that don't work for you. So, for example, the Astra satchel I ordered is a top handle bag that comes with a messenger strap. I opted to remove those and add a two-way sliding chain strap instead and specified my desired strap drop. I choose to color-block my bag with fuchsia, silver, and black leather. I opted for black lambskin lining, dark gunmetal hardware, and added an exterior slip pocket on the back. I just placed the order so I don't have it yet, but I have other Massaccessi bags, and the quality it top notch. Also, the owner, Marco, is an absolute gem, and he really goes above and beyond to make his customers happy. I think the Astra with a sliding chain strap with be the MM style closest to what you are looking for, although it's not a quilted leather bag, so if your heart is set on quilted leather, it may not be the one for you. But I thought I'd throw it out there as an option!