小中大
I noticed that you could get some soluble protein in supernatant(~10-15%). Therefore, it becomes important to think about what is the purpose to purify this protein.
If you want to do crystallization or NMR ,maybe it is worth to try to improve the soluble expression. But I strongly suggest to obtain enough protein simply by increasing the culture volume.
If you want to do some biochemistry experiments, it will definitely waste your time to search methods improving the soluble expression.