ESATA is for storage purposes, not networking. And while USB 3.0 would be preferred, a USB 2.0 Gigabit ethernet adapter would still provide up to 480Mbps. And while you never get 100% efficiency w/ any interface, it would still be a vast improvement over 100Mbps ethernet.
This assumes, of course, that the only problem is the network. For all I know, it might be a lack of processing power on the laptop (or both). So before committing to anything, transfer the file over to the laptop’s HD and verify it runs smoothly w/o the need for network streaming.