Click to select and move with arrow keys could be OK. We should measure times but my gut feeling is that if I already have my hand on the mouse or touchpad (in my case it's always a touchpad) then I can keep using it to move the card around without the extra time to reach for the keys.
Gut feeling again: the keyboard could be more effective on larger distances because each tap of a key is a full movement of one row or one column, and no mistakes.
People using a mouse probably need more time to release the mouse and move their hand back to the keyboard, unless they are left handed: mouse on the left and right hand already close to the arrow keys.
About drag and drop: it's a mess if you can't see both source and destination at the same time. Then you drag hoping to be headed into the right direction. A right click menu could be better in those cases.
Click to select and move with arrow keys could be OK
Oh god no. Like you already state, most people operate both the mouse and the arrow keys with the right hand, so your proposal adds a lot of unnecessary movement. It could work with click to select and with WSAD keys, but most office users wouldn't discover that mode.
I would much prefer navigation keys (arrow keys, page up/down, home, end) to select, shift+navigation keys to move.
My proposal was probably not very clear. The idea is to allow both mouse and keyboard navigation. Which combination of arrows? I'd add hjkl to the list (vi and rogue like games.)
Gut feeling again: the keyboard could be more effective on larger distances because each tap of a key is a full movement of one row or one column, and no mistakes.
People using a mouse probably need more time to release the mouse and move their hand back to the keyboard, unless they are left handed: mouse on the left and right hand already close to the arrow keys.
About drag and drop: it's a mess if you can't see both source and destination at the same time. Then you drag hoping to be headed into the right direction. A right click menu could be better in those cases.