Hello and welcome to Just answer.com, Super mechanic here. About your vehicle.
The vortec engines have an inherant problem with the lilttle poppets on the ends of the injector tubes that will give you those symtoms.
There is a test that can normally be done with the right equipment, an injector leak down test. That will give you an idea of what each injector is injecting.
Before replacing the engine it may be to your best interest to have the injectors checked or cleaned by a GM dealership, as they will have the proper equipment to clean them right.
Here is some of what the service bulletin states.
Some customers may comment on rough idle after start-up, especially if the vehicle has sat overnight. These symptoms may be intermittent. The Service Engine Soon (SES) light may also be illuminated. Current misfire or history misfire codes may be detected with the Tech 2 scan tool.
A deposit build-up on the CSFI poppet valve ball and/or seat may cause the poppet ball to stick open or closed. In either case, the specific cylinder will be mis-fueled, resulting in a cylinder mis-fire condition.
A new injector unsticking and cleaning process has proven to be effective in restoring poppet valves to an "as new" condition. CSFI injector replacement should NOT be considered as a correction for this customer concern.