Juanjo....since the machine is an HX feed to the group, do you have a line pressure regulator valve on the machine or on the line somewhere? I too noticed the flow from the back before centering. So you are giving a couple of warming pulls (are these needed to warm the group or cool the hx?....not really enough to cool the hx so you must be warming). So when you go away to grind and do the fixings the water is cooking hot in the hx part of the machine and building pressure and when you come back and lock in the pf, pull down the lever, you likely may be getting a puck blaster from that first entrance of pressurized water, which will taper off in pressure as you hold the lever down. Your NYC water line pressure is likely at least 3 bar. The HX systems were designed after the straight dipper tube which preinfuses at whatever the boiler pressure setting.....1 to 1.5 bar (1.5 is old school)....so if you don't have a pressure valve to bring the line pressure down to some reasonable level this could be part of the issue. What happens with a higher line pressure is that one tends to grind finer and tamp harder for a lever than one would normally need to do to avoid flow through before the lever is released.
Your warming blasts seem pretty powerful but it may be that these blasts could be better used right before locking in the pf to remove some of the pent up pressure and get a more even ramp on the shot without puck shattering. I also agree with the no headspace idea. If your group screen is curved vs flat you have a self tamping screen which is meant to finish off the tamping and remove any headspace, again old school. Italian barman just grinding and using the tamp horn on either the machine or grinder to approximate the dose and then lock the pf hard to self tamp against the curved screen. So you may benefit from updosing, light tamping, pressure reducing, and why not just change everything????? Just kidding the crema looked lovely and the machine sure looks good.
Just some thoughts about the hardware.

Wow....quite a bit of plumbing there. Does the valve setup give you a constant line pressure? Do you adjust the reading on the gauge with the water faucet valve itself or is there some other mechanism. You may or may not be getting a constant line pressure with this setup, its hard to tell just how it works. I tried reducing the flow and getting it worked out that way but realized that I had the same pressure, just lower flow and ended up getting an actual pressure regulating valve. If your setup delivers constant line pressure I would sure like to know how you made it....seems a masterwork of hydraulic engineering not to mention plumbing fittings!!
Thanks for the shot!