The soggy puck is unlikely to be indicative of any problems. With a Classic, the sogginess of the puck has more to do with the amount of headspace between the (dry) puck and and the dispersion screen. This is why increasing your dose decreased the apparent sogginess. This is a red herring.

You should pick up a gram scale and a properly sized tamper. It is unlikely you will be able to achieve consistent shots until you pick up a scale. The goal is to keep the dose consistent between shots within .5g. A whole bean of coffee is about .1 to .2 grams. It is close to impossible to stay within .5g from shot to shot if measuring by volume. When I first started out I thought it was ridiculous to use a scale but now I don't know why I wasted so much time trying to pull good shots without one.

As to the tamper, it is possible you were suffering from side channeling due to the ill fitting tamper. It's hard to seal the puck to the sides of the basket with a tamper that is too small. You can pick up a scale for about $15 and a tamper for about $30. That $45 will save you tons of aggravation. If you were in the US that is.