I decided to go with this in the end: https://www.amazon.com/20TB-Desktop-External-Drive-WDBFBE0200JBK-NESN/dp/B074R34DD3
This will enable me to transfer all the stuff from my internal drives and have those free for working on Despecialized.
I got it for 15,000 Czech Crowns (about 680 USD), which is a bargain, because normally HDDs cost around 1000CZK per TB.