The ruler part of the square is a bit thin (I suspect this could be part of the cause), around 0.7mm (a bit less than 2/64").
I doubt this is directly the cause. The main reason being that many users of these types of knives are using thin steel rules and squares and not having issues.
Also, over my lifetime cutting, scoring and marking with various knife types against a steel edge I've had many instances of the knife riding up on to the steel and I 100% attribute it to me, due to:
inattention, basically going on autopilot;
trying to work too quickly (a big issue in a production environment) by trying to use a single stroke or,
actually moving the knife too fast.
Doing something unthinkingly, obvious risk there!
WRT trying to mark in one go, this can be fine particularly where you need only a very light line. But for anything deeper one light starter stroke followed by 1-2 further strokes pressing a little more firmly (safer now that the knife has a groove to follow) is always superior according to many sources going way back, and continuing to advice given today by many woodworking teachers.
Outright speed is always going to make control and accuracy suffer, here as in anything1.
also have some aluminum speed squares but I am afraid to use the marking knife (hardened steel) with them since I fear I will screw them up...
Yeah I can virtually guarantee you'll pare some metal off an aluminium square and risk ruining that edge. DAMHIK!
What am I doing wrong?
Possibly a bunch of subtle things which together cause the problem, at least that's my guess. Without seeing someone do something it's really impossible to give better feedback...... and even if you can watch them do it you might be no more confident of diagnosing the issue! I've seen this many times over the years, even with pros giving feedback (in various contexts, including sports and various craft tasks).
What should change?
I have some suggestions, and don't know if any of them but the last will prove useful.
Start again from scratch and try to pay attention to everything you do, including your stance (where you are relative to the knife and the edge you're marking against), then change any of them one at a time and see if you notice an improvement. You've already tried lowering the knife angle, I feel this could certainly form part of the solution for you.
Try knifing a line with your off hand and see if you get the same issue. If you don't, then try to notice what you're doing differently there so you can adopt it with your dominant hand. I've done the opposite when working towards being able to do certain tasks left-handed, not sure if it might work the other way around though.
Watch some YouTube vids of people using marking knives with this edge profile (shouldn't be hard to find them!) and see if you can identify what they're doing differently to you. But don't be surprised if you can't spot anything with at least some of them — the technique that works could be very subtly different to the one that doesn't, and at normal working speed it could be impossible to see that difference.
Last suggestion is the knife itself. If you find you just can't use it for this then don't feel any pressure to continue to struggle with it2. I no longer use a single-bevel marking knife at all for this very reason, having made two I found I just couldn't get along with them. I've defaulted back to a basic Stanley knife or a folding utility knife (these use the same blades) at the urging of a friend who rightly pointed out that they're easier to use, safer to have lying on the bench (blade retracts or folds away), and, most importantly, there's no difference in terms of the marks made in basic knife marking.
1 Going more slowly the instances went down to almost zero, and like I say in my Comment above I haven't cut myself doing this in decades.
2 You might be reluctant to choose this option because the knife is then going to waste. But not at all, you're sure sure to find other uses for it. If you think of it as a double-bevel skew chisel you should immediately see how you might use it to help clean up corners in dovetailing (a common use for spear-point marking knives). And generally it will make an excellent joint-cleanup tool. You could also push it dead flat against the working surface to do some paring tasks, could make a superior choice for paring dowels flush in some circumstances.