Yeah, controlling rockets is counterintuitive, but not hard.
I’m reminded of a story from R V Jones’ book Most Secret War, where in the UK he and a team were looking at intelligence reports about the V2 rocket. Jones calculated that in order to hit anything in the UK the precision needed to align the rocket for takeoff was essentially infeasible. Needing seconds of arc precision to loft the rocket on a ballistic trajectory. Then someone else in the team muttered “gyroscopes” and Jones tells of how suddenly everyone realised that the V2 threat was real and all started shouting “gyroscopes!!”
The Apollo LM had exactly the same issues with off vertical landing attitude as any of the other design. It is just that a leaning over LM doesn’t look very dramatic because it is so squat. But 10 degrees of lean is 10 degrees of lean, and your guidance system has to be able to manage it on liftoff no matter how tall your vehicle is.
Luckily for Apollo the basic technology for guidance was already well understood, thanks to the ICBM projects. The Apollo guidance system was more advanced than an ICBM in every respect, but this was a matter of scale, not intrinsic technology. In order to navigate in 3D space the guidance system needed an additional gyro axis (and arguably could have usefully had a fourth to avoid gimbal lock, but that was a nice to haver and would have added significant size.)
The Apollo guidance computer was a minor miracle of miniaturisation and genius level electronic design. Not just the processor, but the peripherals and ancillary equipment. The CSM and LM had identical AGCs and gyros and acelleromter systems. Moreover the LM had a standalone guidance computer that had one job only, get the LM back into orbit where they could be rescued by the CSM. The LM could track the CSM in orbit and control the ascent to match.
There was, in addition, the Saturn V’s guidance system that resided in a ring atop the booster just between the LM and the rest of the Saturn. Famously, when the Apollo 12 launch was struck by lightning, dropping the entire CSM electrical system off line, including the guidance computer, the Saturn just chugged away and lofted the payload exactly as needed. That sustem was different again. Built by IBM it was much larger and heavier, and very simple - not really being a fully fledged computer system. But robust.
Any issue with guidance and managing launch from the lunar surface was a solved problem no matter what the actual vehicle used was. A big tall rocket looks as if it should be much more precarious, but assuming it doesn’t simply fall over on landing (something some modern unmanned missions have had problems with of late) launching form the surface isn’t an issue.
Controlling a rocket is the same problem as balancing a broomstick on your hand. A bit of practice and you can tune your reflexes to make it look trivial. An electro-mechanical version of this is a staple of undergraduate control theory labs. Students get to code up the control law, work out the parameters, and get the machine to swing the stick upright and keep it there, even when you push on the stick. Very satisfying.
This is also why rocket motors are on the bottom of rockets. Counter-intuitively, this is where they must be for control to work. Intuition would suggest that putting the rockets at the top and pulling the craft would be more stable. But it isn’t. The system will develop worse and worse oscillations as the pendulum effect of the vehicle hanging down dominates.