Intent
I understand your point of finding ways to continue the stay, and there is nothing wrong to do that.
To make things clear: H (or L or O) type visas are considered 'dual intent' visas. Although you are given it for a temporary period, INS knows that you may have an intention to immigrate to USA.
For the other visas, e.g. B (Visitor or Business), F (Student) visa are clearly for a temporary period, and can be denied if you show any intention to immigrate. If you know yourself or anybody's case who tried to get these type of visa, they have to show some proof (like assets, other family ties etc.) to the Consular in their home country that they WILL return back, and will not stay back in the US. If the consular is not satisfied for whatever reason, s/he can deny your visa application.
As stated, H is different, and you don't have to prove to the consular any such ties to your home country that you will return. It is assumed that you MIGHT stay back in the US.
This why, once you have applied for LC, INS knows that you want to stay back in the US, and it contradicts the ground for F-1.
I think EB3 is not a bad thing as long as the Priority dates remain current. Of course, the wait is longer to reach to the 485 stage, but with the new rule of filing 485 concurrently with 140, you will be not have any major problems.
Is your 6 year of H-1 expiring in 3/2003?
I think we can continue discussing here so that it might benefit others also, just in case ...