But the docs seem to say it’s supposed to be arc seconds?

This is way outside my area of confidence, so I may be completely off the mark, but why is RotZ given as about -77° (which seems consistent with the R01-R31 values, assuming they form a matrix), but +rz is -85° ?

There’s something funny going on with your latitudes — where is -122° supposed to be?

What if b or d are non-zero?

In my example, x_g1 and y_g1 would be your longitude and latitude.

This smells like a datum conversion issue, but I am not familiar with R, so I can't say for sure. I notice that the spTransform docs mention that the behaviour w.r.t. datums has changed.

Xpixel and Yline are the column and row positions, respectively, of a pixel in the grid. Notice the paragraph a bit further down about corners vs. pixel centers.

You are obviously suffering from some sort of coordinate system confusion, but it is hard to tell from the question exactly what it is. Could you give a concrete example of one of these bounding boxes, what coordinate system it is in, what coordinate system you want it to be in, and roughly what part of the Earth you expect it to cover?