There are two city firms who have the accreditation to train in-house solicitor advocates. One of them is HSF. The simple truth of the matter however is that if you are going to go to trial and the consequences of an adverse finding is billions of pounds for your client, you'll probably instruct specialist outside counsel.
Also, do you know where I can find more detailed information about employment opportunities for solicitor advocates?
I'm not too sure on this. The problem you may have with trying to get into these MC firms who can train you is this:
Why do you want to be a commercial lawyer?
If any of your answers involve wanting to be a solicitor advocate (in which case they will ask you why you don't become a barrister), or because you want to do pro bono (you can imagine how this would go down) you are going to struggle.
I'd say, your wish (if it is so) to join a big city law firm, and to gain higher rights of audience, are probably incompatible to a successful application to these firms.