Now that's a VERY interesting way of thinking about it.

It's the proper and textbook way to think about it.

difficult to keep the ball exactly centered in a 50-degree bank, so
I started thinking about whether it's even possible to do this in a
60-degree bank.

Of course it is.

However, in a steep bank, the rate of turn is mostly controlled by
the elevator.

No. The rate of turn is controlled by load factor at a given
airspeed. You can increase the rate of turn by banking more, or you
can pull back on the yoke to increase the load factor (temporarily).

In a 60 degree banked turn, you will get a load factor of 2 regardless
of what you do with the elevator. If you don't increase the AOA
during turn entry however, the aircraft will accelerate and the 60
degree banked turn will occur at a higher airspeed, in a rapid
descent.