What does your contract say? What model set do you have? When you say convg switch do you mean convergence output IC? There is no convg switch in these sets. Is the servicer mitsubishi authorized and does he have lots of experience with these sets?
Do not assume. Ask. Review the language of your contract, speak to a supervisor if the person on the phone cannot answer your questions, and demand what the contract states. Tell them no way you will renew if they do not live up to the contract. Make sure that the servicer is experienced on the sets and a Mitsubishi ASC. If they are not relay your concern to the warranty people and let them know that you will hold them to the contract whether the servicer is qualified or not. Be polite but insistent on clear answers. Make notes about every contact and get names and direct phone and fax numbers if possible. Escalate to a supervisor when they cannot give you answers.
Is it a convergence problem? Go to the convergence pattern and see if the colors line up to make a white line. What you are describing sounds like neither a convergence issue nor anything that having an HD receiver will solve. It sounds like the tech did not solve the problem that was your complaint and you need to talk to Philips again. If the pix is going out of focus that is one problem. If it is going out of canvergence that is another. You need to identify what is actually going on.
Did you determine if the servicer is a Mitsubishi ASC? Are they reputable or some guy working out of his garage? Who is the servicer?