H - there’s a plugin that does exactly what you want to do (drawloop plug by clacos) - but it’s not been updated for a while 
In the meantime - Cut - RMB option will let you slide the new vert from 0% to 100% along the appropriate edge.
This has to be done one edge at a time - and you then have to select the new verts and use connect.
If you do one of these RMB Cut ops, then select your next edge and press either D or Shift + D (repeat last op / repeat last op with drag) - things can be speeded up a little 
You need advanced menus on, btw.
pp