Seems like an interesting project... Yeah the stock TW does seem to have a short wheelbase....so I can see how it'd be a bit flippy.
14" though is a LOT. Like...a lot of the times you'll see folks hillclimbing CR500s with only 6" of extension...granted you were a little shorter to start with, I don't think 14" is a great idea...certainly not as a starting place.
Also - I would imagine the bike would be nearly useless as a trail bike anymore. You'd have such an enormous turning radius I don't think you'd like it at all. And you'd have to spend several hundred dollars trying to get a shock to behave vaguely appropriately with a swingarm that long...
I would suggest a considerable amount of caution. And also, maybe look for a way to create removeable and/or adjustable extensions. Granted that it looks like you've already made your cuts in the swingarm, maybe instead of welding that all together you could make smaller inserts that would seat inside the box section of the stock swingarm a bit and be bolted in on both sides - and then you could try out a modest extension, and if you decided you needed more you could just make longer ones, and bolt them in instead.
The other thing to keep in mind is that all of this is a game against weight transfer and the fulcrum point of the overall assembly...which is to say that sure, 14" of extension would probably make it all but impossible for the TW to flip over, but you're also going to be getting close to no traction anymore on that rear wheel as well...so while you're safe from wheeling going up a steep hill, you're likely to just get stuck halfway up with a spinning rear wheel. On a bike that takes an acre and a half to turn around.
At any rate...I think the important thing is to start small. Maybe like 4" - you'd be surprised how much difference only a few inches would make. And you're going to have to either have your shock modified to accommodate the new length, with a new spring and valving - or buy a new shock outright.