The Twins rig will stream instantly as soon as you let go of the sheet and is a vast improvement over any other downwind rig I've ever seen - BUT - it is pretty much a downwind only rig. Even with leeboards and a rudder added, it most likely would be a pretty poor general purpose rig.
The lack of ability to move around in the boat at all is problematic. You could use a spritsail with a brail eyelet to jiffy-furl it when needed, but it's not a particularly neat or efficient furl. Fine for launching and landing, but not really something you want to leave flapping there all afternoon. A balanced lug has three spars, but they tend to be substantially shorter than those on a lateen. With parrels on the yard and boom around the mast you can usually raise or lower it very quickly down to gunwale level is a few seconds. It's easier if you're close to the mast, but it could be rigged to operate from the stern with a bit of work. In terms of getting the sail up and down fast and leaving nothing to cause windage aloft but a mast, it's probably the best bet.
The problem with most Bermuda-style sails (3-sided, typical sailboat-sail-shaped) on canoes is that they usually end up being awfully tall by the time you have adequate sail area to do the job, and that brings a lot of heeling force that you don't want.
In the "outside the box" arena, did you ever notice the profile similarity between a lateen sail and a big boat's Genoa? I suspect that you could rig a mast and hang up a sail similar in size and shape to a lateen, but on a dinghy headsail's roller furler, like a genoa. Release the furling line and pull the sheet and the sail unfurls. Pull the furling line, easing the sheet and the sail rolls on it's stay in a neat bundle. Use the halyard as a backstay when the sail is up and if you want to minimize windage, ease that and lower the rolled sail the gunwale.