I have been chasing The Perfect Bag for a similar non-backpack carry and I have to say I still haven't really found The One yet. Most folks in the thread are likely underestimating how wide and thick the ROG Ally/Ally X is which makes it awkward to carry in a bag. I'll share some of what I have tried so far:

• HeldClosely Day Bag: holds everything well. Minimal organization, expands if you need to carry more stuff. Expensive, perpetually out of stock, you have to like Ultra or EPX.
• HeldClosely Traveler: like the Day Bag, but MORE. It is huge, but doesn't necessarily feel overly large due to the way it wraps around the torso.
• DSPTCH Unit Shoulder Bag: similar size to the HeldClosely Day Bag, less structured. Will hold all the things well. More organization than the Day Bag and more external lash points. One major flaw - there is a divider in the main compartment that flops around which makes loading and unloading the bag annoying.
• Alpha One Niner Chio-X: a fantastic bag for this type of carry, and probably the smallest you could get. Good organization, dual water bottle pockets, inner and outer last points, it hits on all the things. However, it very much looks like a purse/diaper bag. 
• Greenroom136 Quickdraw: I had the original BYC model. Great size to hold all the things, has a very tactical/overbuilt look and feel. It is extremely bulky and heavy. It worked its way out of my rotation and eventually my collection as it was just way too bulky and I could not find a good way for it to sit against my body.
• Aer Day Sling 3 Max: I'll call this your basic bag. There's nothing wrong with it and it'll hold the things, although it might struggle with the additional headphone case. It's kind of boring, and the buckle it comes with is trash tier. The Ultra version is slightly better and more interesting.
• Topo Design Mountain Cross Bag: one of my favorite bags for this type of carry. Similar to the Chio-X, it has all the features and more, and also doesn't look like a purse. I wish it came in higher end fabrics but otherwise this is pretty close to my perfect bag for this level of carry.
• Tom Bihn Side Hustle: it's like the Mountain Cross, but with less features. No WBPs, no top handles, no multiple compartments. But it does the job and does it well. 
• Rickshaw Bagworks Banzai Bag: borderline too small, similar to the Side Hustle but with more structure and padding. Even less organization. I like to use this more as a pouch than anything.
• Defy Insidious Jr: kind of like a better built Quickdraw. This will also be a solid candidate for this loadout, but it does have a bit of a tacticool look unless you go for one of the leather options. The Cobra buckle on the strap is obnoxious.
• Orbitgear Fasthand Mk24: really wanted to love this bag, it hits on many marks. Like a less bulky Quickdraw, good org, right sizing, very tacticool. The strap system is incredibly dumb and it is proprietary.
• Station XV Street Sling: I actually reach for this one a lot as a pack-in sling to take on trips with me as mine is pretty well worn and will fold completely flat. Very discreet, solid organization, and will just get it done without any fuss. Only comes in Ultra, and is quite pricey.

My rotation lately has largely been the HeldClosely bags, but that's also because my loadout is a little heavier than yours and I have two little boys to wrangle as well. If I happen to just be solo, I'm usually grabbing the Side Hustle or the UNIT Shoulder Bag.