Would it be possible to make the 'alt' rotation relative to the angle of the camera, rather than the angle of the object you're rotating? This just hit me as something that might make that mechanic feel more consistent, even though it's only really needed to get objects unstuck.
chiming in behind Slipcor for a differing point - rotation can help some things fit better into small places, like shoving an entire log into the smelter before hacking it to pieces so you don't have to chuck each piece in individually (once it's wedged in a small bit, use another log or crate to tap it in, like a mallet hammering in a peg)
Additionally, I like to stuff my smelter fully of ore, and then turn the box 45* so that it catches the ingots while I do other things
then I carry the box full of ingots to the forge, lit er up, and heat the entire box of goodies all at once, tilting it over towards me while I'm waiting so they're easier to grab out of it. (90* side rotate, open to anvil)
I also like setting delivery boxes ontop of crates so that most of the items fall into them, and then use the crate to dump them on a smaller area that the delivery box couldn't fit.