The reason Dan said what he did about your flush is that on HX machines, the flush should happen immediately before you pull the shot (depending on the machine of course) as the temperature in the HX will start to rise after your flush.
Try this experiment. Using a digital thermometer, flush two ounces into a cup and temp it. Wait one minute and repeat. Chances are they will be the same temperature, so if your machine is running hot then your one minute before flush doesn't accomplish what it is supposed to. A high temperature can also cause a faster extraction. Something to think about. Also, the hot water spout (i believe) pulls from a different reservoir than your group head, so you should not count that in your overal flush routine.
Don't worry about using your hands in the coffee...this is how it's done. (for the most part) Walk into any one of the highly respected cafes talked about on this site and you will see baristas using their fingers and hands to level and distribute the coffee. If your coffee is tasting okay, but running a little fast, I would recommend that you a) use a little more coffee or b)grind a little finer. You do say that your shots are sweet, but a little sour. This sounds like classic underextraction. The above should help you remedy the situation. IF your machine is running cold, this could also cause the problem. But let's tackle the easy to fix problems first.
Tamping harder should have a negligable effect on your overall shot time.