The boat is currently a day sailer.
If you were to put Arne’s rig in it and do some day-sailing next summer you would probably be making a good start.
If that doesn’t appeal, you could go ahead straight away and increase the size of the cuddy somewhat, as you have planned, give it the rig Arne suggests, make a secure compartment below the floorboards for carrying heavy stores, a place to stow a tent or canopy, somewhere for sleeping bag, cooking utensils etc etc - and then I think you would have a pretty good camper-cruiser. Careful placement of reserve buoyancy will add to your confidence. It will enable extended cruising if you watch the weather. Once out on the water you will be able to push the boundaries a bit and judge for yourself what the limitations are. You won’t be lacking opportunities to experience stressful situations. That’s as far as you can take that hull, in my opinion – but it’s a very long way from merely a junk rig conversion, and a very long way from merely day sailing.
The rig will be good, but in my opinion, ultimately you will find that the hull is not ideal for “…potentially nasty environments for long periods of time…”
But it will be a good enough platform for preparing yourself and planning for that.
In other words (your own):
"...I see this boat as a training ground for the next boat... ...So, it's worth it to put in a little extra effort to make the boat something a bit more capable than the fair-weather daysailer - the comfort in knowing that I can push her (and myself) in ways that foster slightly more significant mistakes and learnings than one would assume from a typical open dinghy..."
Best of luck with your project.