I've done several dozen BIAB batches and have never burnt a bag. I have sewn up three bags so as to have one ready for the 2nd batch on brew day w/out worrying about thouroughly cleanly the first- and then a 3rd in case one bursts, about which I've read, but fortunately haven't had occur. I double and triple sew the voile and have done just under 20# grainbills with no problems at all.
I use a ~15 gallon kettle that came with a basket, but I just don't see the need for it. Usually hit about 4 degrees above the target temp, cut flame, then insert bag, then grainbill, temp drops approx. the 4 degrees. Cover with blanket. Usually lose maybe 1-2 degrees if any over 60 mins. The few times I have had to refire a bit, I pull up on the bag at the top a bit so it is not stationary while being fired.
Unless you completely remove the inner keg ring, I don't see how you could get a large enough basket inside to be able to get a 15lb + bill around in it.
Just my thoughts.