Nice job! I almost mentioned trying to use the old batteries. I'm glad you got it out of protect. I never tried connecting the smart charger as I figured the lab charger would do everything I needed.
I used the EG4 WP 48V 100AH (with the new 200 amp bms) and had the same issue on the initial key turn. The main relay would 'chatter' and the battery would go into protect mode. I got an adjustable time delay relay with a 12v coil and another larger relay also with a 12v coil. Smaller relay...
I did my conversion with this exact battery. It fits perfectly without any modification. I added some dense foam to the sides of the battery tray to lock the battery in and a pull strap over the top to the frame to hold it down (though it's nice and snug in the foam with the battery tray clamps...
Looks like your battery has the new COM port on it. Supposedly it allows communication with the BMS. Mine first battery got locked in protect mode and they had to replace it since there is no way to access the battery without cutting into the case. Did your battery come with any literature...
Since you don't have any voltage at the terminals it's unlikely any smart charger will work. The typically need a voltage at the terminals (and usually around where the battery "should" be) before they will turn on. You could try a "dumb" charger. I used a lab power supply to send 48V to wake up...