Your protein is not soluble in the conditions you are trying. When a GST tagged protein leads to the 25 kDa band and not full protein, that means that the cell does not like the protein (either toxic or insoluble, or not properly folded) and it is cleaving it. GST is not a tag that improves folding. It is a tag tag gives false solubility. Better use a MBP tag or a NusA tag. Here a paper talking about this:
http://www.ncbi.nlm....pubmed/16168669 (let me know on private if you cannot access the article, I can send it to you)
You have already tried different expression conditions in this vector. People usually start with 3 different tags in 3 different vectors with different promoters of different strengths (hence they clone in parallel 9 constructs) to try them:
http://www.ncbi.nlm....pubmed/20814932
http://www.ncbi.nlm....pubmed/18678258 (this one has a nice scheme on the second page about what I mean above)
You can also try chaperones system (co-expressing your protein with different chaperones)
http://www.takarabio.../pdf/hd/BV1.pdf
Or in ArcticExpress:
http://www.genomics....tail&PageID=467
since chaperones do not function at low temperatures, in these cells people have cloned some chaperones from sychrophilic bacterium Oleispira antarctica. This makes it possible to both use chaperones and low temperatures.
Another thing you can try with the construct you have now is the autoinduction media, sometimes in this the protein is folded better:
http://www.ncbi.nlm....pubmed/15915565
There are many things you can try. There is no direct way than trying. The order is up to you. Good luck,
Andreea