Hmm,
When I pull a double on my La Peppina, I do a couple of partial pumps until or hopefully just before a drop comes out of the portafilter spouts to load the puck with water for a ten second pre-infusion. I push and hold the lever down during the pre-infusion and then release it after ten seconds. I find that this gives me a full extraction and good crema that I wasn't getting when I didn't pre-infuse. It also loaded up the head and puck with water so that when I released the lever for the extraction there was no need for additional pumps, in fact I would usually pull the cup before the lever reaches the top as the shot starts to blond. This may be due to the fact that the La Peppina has one of the largest
single pull volumes of the manual espresso machines.
For a single, I don't do any pre-infusion or I get an over-extracted shot. Instead I do a quick one or two partial pulls to load the group with water and then start the extraction from the bottom with no delay. I also stop before the arm reaches the top for singles, but we're dealing with only 7 - 10 grams coffee in this case.
As for all your shots having a similar taste, you might want to pull and soak your dispersion block to remove any built-up crud and also make sure that you're using fresh beans since I would imagine that stale beans would have a more similar taste. A regularly used espresso machine would probably have less problems with oil build-up affecting the taste as one that's been sidelined where the oils have a chance to become rancid. I've heard that for grinders, regular cleaning becomes more important for irregularly used grinders for the same reason.
I hope this helps and let us know how it works out. My La Peppina got moved to the garage for Christmas and I need to pull it out and fire it up this weekend. I'm thinking of checking the dispersion block now that I've written this, though I think I cleaned it just a few weeks ago.