Why does my new little shunter stutter on the points?

You're not overthinking it, and it's not just a fact of life at Z scale either. What you're describing sounds like the frog on those turnouts. On an older DC setup the frog is often dead or unpowered, and a tiny switcher with maybe four wheels picking up current has almost no margin to coast across that dead spot. Your HO stuff sails through because it's got more pickup wheels and enough momentum to bridge the gap. The little red shunter has neither, so it stalls the moment it loses contact.

Two things to check. First, look at how your turnouts are wired. If the frog is dead, you can get a small slide switch or a simple frog juicer to feed power to it, wired so it flips when you throw the points. That alone fixed this exact problem on my shelf layout. Second, throw the turnout by hand and run the loco through slowly while watching the wheels. If you see one wheel drop or lift at the frog, the flangeways might be a hair too wide for Z flanges, and a tiny bit of filing or a shim can help. Cleanliness matters more at this scale than people expect, but not because the track is dirtier. It's because the contact patch on those wheels is minuscule, so a film of oil from fingerprints or dust that HO wheels ignore will knock a Z loco out. Wipe the rails with isopropyl on a cloth, and handle the wheels by the body, not the pickups. I keep a small block of track cleaning foam and run it under the loco every few sessions.

As for weight, yes, some Z scalers do add tiny strips of tungsten putty over the motor or under the shell if there's room. It helps with pickup pressure and low-speed running. Don't glue anything near the drivetrain though, and test it on a straight before you button the shell back up.

One more thing since you're planning a shelf layout: keep the curves generous and avoid mixing rail heights between sections. Z punishes rough joints way more than HO does, and you'll thank yourself later.

Same thing happened with my little Z switcher, and the dead frog explanation was spot on for mine too. I ran a couple of feeder wires from the power bus to the point side of the turnout and the stalling stopped straight away. Before that I could watch the headlights flicker off as it hit the frog, which made it obvious it was losing contact there. If you've got a multimeter, touch it to the frog while a wheel sits on it and you'll see right away wheather it's live or not.

Following this one closely since I'm in a similar boat, just with N scale instead. One thing that helped mine that I haven't seen mentioned yet was cleaning the wheel treads themselves, not just the rail. I used to only wipe the track and wonder why the little loco still stuttered, then someone at my local club pointed out the wheels pick up grime off the layout and carry it around with them. A quick roll across a paper towel with a bit of alcohol on it made a surprising difference. Also does anyone know if these tiny motors mind sitting idle for weeks at a time? Mine lives in a display case between sessions and I'm wondering if that's part of my problem too.

One more culprit to rule out, the point blades themselves. Even with the frog powered, if the blades aren't bearing firmly on the stock rail the loco is only bridging through that one contact point. My Z switcher had the same hesitation pattern and it turned out the blades had gone slack from years of hand throwing. I gently bent each one inward so it presses tight against the rail and the stalls vanished. Took about ten minutes with a pair of tweezers. Worth checking before you start adding weight, since a slack blade will still bite a heavier loco but will drop a light one instantly.

Not sold on the weight advice from earlier. My Z switcher stalls were never about mass, they were about contact. Bolting extra ounces on does nothing if the loco is only picking up from two or three wheels and one of them is over an unpowered spot. What actually helped mine was a set of pickup wipers off a donor chassis rubbing the backs of the wheels, so now there's always somthing live touching rail. Have a look at how many wheels on that little red thing actually carry current before you start stuffing putty under the shell.