Once I finish the conversion I usually do NOT wish to quantize as I want the vocal timing to stay as it was recorded. BUT, whenever I make any changes such as moving a note I lose the connection between notes and it can be cumbersome to restore it. There may be a better way but this is how I do it for a quick solution!
set Interface Scaling to 150% to make it easier to see connections
With snap turned off you can also simply click/highlight the note(s) you want (within a connected series of notes) - hold down SHIFT - and then drag the note to another pitch. It will freeze horizontal position - not move its timing, thus staying connected.
Unless I’m misunderstanding this thread which I only read very quickly.