Mounting a set of fully-encrypted drives with a single password prompt upon booting

Question

I have a laptop with a single OS installed on SSD (C:\, Windows 10 Pro + programs and apps, no multiboot, no GPT), secondary HDD (D:\, my files and libraries) and an external USB-HDD (E:\, for backups only).

I would like to set up a full-disk encryption on all three drives so that:

1. The password is the same for all drives and is to be entered only once upon booting (not counting Windows logon screen, of course), which results in automatic mounting of all drives before Windows starts;
2. If Windows 10 fails to boot, the content of all the drives should be easily accessible (e.g. one should be able to decrypt them) from another computer or from Linux LiveCD/LiveUSB;
3. No wiping is required.

I used to use DiskCryptor for this and it worked fairly good for parts 1 and 3, but I could't figure out how to get access to the files from a Linux pendrive once, when the only things a had were the computer with a Windows refusing to boot and a LiveUSB drive with Linux, and I needed my files ASAP.

For the same reason it seems like going with a built-in BitLocker is also not an option. Veracrypt, on the other hand, would assure parts 2 and 3, but I cannot figure out how to mount a set of drives at once alongside with a system partition.

Is there something I'm missing, and what's the best way to mount several encrypted drives at once?

I apologize in advance if the question seems to be too broad or off-topic here. I'm not an expert in computer security and I tried to solve this problem for myself for a while without 100% of success.