That won't work for a couple reasons... One, you NEVER install any toothbar accessory on a material bucket because structurally, they aren't strong enough to take the strain in the center with out bowing. Only use an excavation bucket with a double sheet floor.
Two, when you attempt to jack the deformed floor back down, what will happen is, as you apply pressure to it, it will pull in the side sheets and most likely crack the welds.... and, you will never get the floor parallel to the bucket again anyway. Has to be heated and straightened. Cold forming will not work satisfactorily.
On the side, I rebuild buckets that have been abused like that and you have to cut the side sheets away and reweld them or the bucket will always have a smile in it. Not just small tractors either, I do wheel loaders as well. You'd be amazed how buckets get abused.
My suggestion is always buy an excavation bucket versus a materials bucket. Every brand of tractor builders offers them