Assuming the batteries arrive with some useful charge, I think it would be fine to charge each one full, one at a time, using solar. You can connect the first battery, configure the all-in-one appropriately for the battery type, connect the solar, and let the battery charge. Disconnect the solar, disconnect the first battery, connect the second battery, reconnect the solar, charge the battery full. Repeat for the remaining batteries. One all 6 are full, disconnect the solar, disconnect the last battery, wire up the 6 batteries in parallel, hook up the all-in-one, hook up the solar one last time, and enjoy.
The above would be best if the 6 batteries are all at different SOC when you get them. If they are all really close to the same SOC, then you could probably just hook them all up in parallel right from the start, hook up and configure the all-in-one, then hook up the solar, and start charging.