Lapavoni ! I love mine !
The time it takes for water to percolate through the portafilter on tank pressure alone is the best measure of your grind/tamp combination. I shoot for 4 to 6 seconds. Then I let it drip (?pre-infuse?) for 10 seconds before pulling down the lever.
If water goes through too fast, make the grind finer or tamp harder. If water takes too long, make the grind courser.
There is a continuum of grind/tamp combinations that can give the 4-6 second effect. But too of a course grind with really hard tamp gives weak extraction. Also, you get very little crema.
There is nothing wrong with your 51mm diameter tamper. My tamper is 51.7mm, with only a few ‘thou clearance. I made it on a metal lathe for a custom fit. But even a small bit of grounds on the edge and it jams. I need to wipe the edge every time I use it.
I know many caffeine-heads poo-poo tamping scales. But you cannot get consistent performance without it. It doesn’t matter how hard you tamp, but it must be consistent. You can jerry-rig a scale. Get a wooden ruler and put a pink pencil eraser under each end. Put your portafilter half way and tamp until the ruler bends enough to touch the counter. If you want a harder tamp, move the erasers a bit closer together.
Another hint: The brew head is a big chunk of metal which will cool the water and under-extract if the head is not pre-heated. Run a full shot of water through the head to pre-heat before pulling the first shot.