Since you're transposing notes you'll probably find this Mouse Modifier behavior quite helpful:
Context: [MIDI note]
Mouse gesture: [left drag]
Modifier: Shift+Ctrl
Behavior:
"Move note on one axis only"
Here it is pictured in REAPER's Preferences window:
Check out all the other Mouse Modifers and Actions for the MIDI Editor. There are a lot of very useful options!