The only reason something
The only reason something breaks while temperature is on the way up is thermal shock. We have a good tutorial on thermal shock on this site here:
If the piece was not properly annealed on the previous firing that could contribute.
It is possible that peaking might have done it – but you would have likely heard the break if that was the case. From your description it sounds like it happened before you looked.
Always fire as low in the kiln, and as far away from elements, as possible since that gives you the most even heating.
Yes – you can refuse and reslump.
Helios Kiln Glass Studio