What I meant is that most people set the start of their employment to 7/1 as they finish their residency on 6/30. I would suggest to set the start of your employment on the H1b petition as 7/25. You are still legal (within the J1+30day period) and if your H1b or waiver don't come through on 7/1 (due to the high volume of cases on that date) you don't run into this 2 week thing.
Now, I don't want to give you any 'advice' that can get you into trouble. You need to be employed for 3 years at your waiver location before you can move. So if you are planning to leave your employer, you will probably have to bite the bullet and get a H1b extension with that employer and file for a H1b transfer a couple of weeks later. You need that 3 years of employment, come icy-rain, locusts or high water.
Now for your contract issue. That is a tricky one. Your employer might try to blackmail you into another 2-3 year contract over the 2 week issue. I would just get the H1b paperwork ready with a 2 year time on it and get him to sign it but avoid getting a new contract with him. Then just don't sign whatever he puts in front of you.