It's simple: Encrypt all your systems
If you have hard disks, you can securely delete them by writing random data to every location. There might be some spare area that is used to replace defective sectors, but not that much and replaced sectors are defective anyways, so this should be secure enough for you. But for your scenario, this doesn't seem to be that adequate. If you have a 4TB disk, you'd need about 3,7 hours to overwrite it, assuming a constant 300MB/s rate. If you get the information the government is searching your home, do you think they'd wait a few hours to let you delete your data?
If you have SSDs, it's even worse. You cannot reliably delete them. SSDs have more storage than advertised to the system. They use this for overprovisioning to replace defective cells, as fast cache and for wear-leveling. There is no reliable way to delete all data. The SSD might look empty or filled with random data after you "cleaned" it, but someone reading the flash chips inside will still get parts of your data.
There are newer SSDs which can be securely deleted. They work by always encrypting all the data on the SSD. If you don't set a key, they just store the encryption key in plain. If you want to clear the data, this key is deleted, everything on the SSD turns into garbage.
So there is no solution but encryption for you. If you have new SSDs and trust the manufacturers, you can just wipe it with a command. Usually it is the secure erase command, but you have to make sure that your SSD really uses hardware encryption before, else it won't delete all data (or for some drives it doesn't actually delete any flash cells, just marks them empty in the controller).
The most secure way is to use your operating system encryption tools.
For your use case, you can configure the servers to automatically unlock the encrypted drives by storing the key in plain. You just need a way to securely delete this key fast. The most secure way would be to use a smartcard, but storing it on a HDD should also work. (NOT a SSD, unless you can securely erase the whole SSD)