moveObjects cheat

Unfortunately, moveObjects won't let you do that. However, I'll provide you a helpful cheat sheet you can use.
Though remember, rugs will always snap to the grid no matter what. My suspicion is it's because rugs become part of the floor once placed.

If you have Mansion and Garden stuff, you can use this cheat:

setQuarterTilePlacement 

This allows you to place items more freely by pressing Control+F. If you want them to snap to grid again, you can simple press Control+F again.
Why I recommend this cheat is because you can toggle it without having to enter it again and you can simply type in setq and press tab key to have the game fill it in.

Though if you don't have Mansion and Garden stuff, you'll have to use this cheat:

boolProp snapObjectsToGrid 

This is like pressing down the alt key in the next games. If you want to turn it off again, you'll have to type in this cheat again.


And sometimes you want to have objects be diagonal. There's a cheat for it too.

boolProp allow45DegreeAngleOfRotation 

This allows you to rotate objects 45 degrees by either pressing . or , keys.

Though I do warn you that some objects may become unusable then diagonal or if it's off the grid. I'd always recommend to test out if it works the way you want.

@EgonVM
Thank you so much, this was so helpful.