EDIT: I found this: https://www.ebay.com/itm/304479674540
Can this be used together with 2xSATA-to-eSATA cables and external eSATA enclosure?
Yeah most will just use a desktop, however a laptop with an eSATA port can also work just as well for a portable solution. AFAIK with eSATA, you still need to avoid most enclosures or docks because they often still have a bridge board that can cause the same issues as USB. Instead I think the best solution would be:
The destination drive is fine to connect via a standard USB adapter, so you don't need 2 eSATA ports or anything like that.