The BlueNova have a built-in BMS, but if you read in the other thread I linked, it seems they need to be disconnected and reconnected after load shedding to get them to start charging again.You can't charge a lithium battery using a lead-acid charger also you need a BMS.
Open it up, you might be able to bypass the PSU and run it on 12V and 5V, or maybe even 12V only.The Synology is a problem because it has a 220v AC input only.