Interesting, I don't have any experience with the flake form. I wonder if it's similar to the type Susan gets in Canada . . . I think what she gets already contains some stearic acid. So for that reason it sounds better for a shampoo bar application and the powder version sounds better for a body wash where you want it to dissolve completely.
Anyway for what it's worth, the prill version I have took some heat to get good and melty but it never completely liquified. If yours contains stearic, it may need even more heat than you think.
As far as the 1:3 ratio of SCI to coco betaine, that sounds lopsided to me. My coco betaine is quite watery so 3 parts of that to 1 part SCI seems like it wouldn't make a good detergent bar. Your 1:1 ratio is more what I had in mind so keep us posted on how it turns out.