[VBprogrammer]

> In the previous generation of 737's, there were exactly two things outside the wheel that could control the stabilizers

It doesn't take anything away from what you've said really but there is at least one other system which can control pitch trim. The Mach trim system counteracts changes in the centre of pressure due to speed by making adjustment to the trim.

> Now we have three systems that can control the stabilizer wheels, and the new one doesn't have a labeled switch, nor was anyone told it existed.

Just to add to this point, I believe the reason this was done this way was an attempt to keep the control behaviours of the new aircraft as similar as possible to the old (despite having more powerful lower slung engines) for the sake of maintaining training consistency.