Yes, the search for sweet, carbonated cider continues. This is my approach... you might find it useful.
For the past month or so I have been running a comparison of AS-2 and TF-6 yeasts which Fermentis claim will leave some sweetness. They certainly do... not a lot, but enough.
Using the same blend of AJ, both yeasts produce a fully fermented (SG 1.000) pleasant off-dry cider with no back sweetening needed. I prime by gravity reading on the basis that two gravity points will ferment into about one volume of CO2. In fact, with the first AS-2 batch, I primed from 1.000 to 1.005 using the original juice as the source of fermentable sugar, bottled then left it for a couple of weeks. CO2 production stopped at a pressure of 2 bar (approximately 30 psi or two volumes of CO2 which was what I expected since by that time all the priming sugar should have been converted to CO2 and alcohol).
However, to continue the exercise I also primed some of the fully fermented cider to 1.010.. This was bottled (with a monitoring pressure gauge in a test bottle... a more technical version of a soda bottle squeeze test) and heat pasteurised when the pressure reached 2 bar. The remaining unfermented sugar (about 10g per litre) resulted in a medium-sweet cider.
Attached FYI (pictures are better than words... whoops, its filename is labelled 2021 and should be 2022) is my pasteurising chart for one of the batches so you can see what I am on about. Although I do monitor time and temperature it probably isn't really necessary since I find that heating bottles of cider from 60C to 64C in a constant 65C water-bath takes about 8 minutes and generates around 25 pasteurisation units (PUs). It is generally accepted that between 30 and 50 PUs will stop any further fermentation and also destroy pathogens... win-win.
After removing the bottles from the hot water, their residual heat generates another 20 or so PUs as they cool back down to below 60C. With this approach, bottle pressure at 64C and 2 volumes of CO2 doesn't get to much more than 80 psi so the risk of bottle bombs is minimised. You will get similar results if you follow Pappers' sticky at the top of the forum.
If all of this sounds like gobbledegook, have a look at the attachment to my post of 1 Feb 2021 which goes into detail about heat pasteurising. The point of this post is that without too much effort you can produce a stable sweet, carbonated cider without the risk of on-going fermentation. Hope this helps.