Does anybody make an adapter to convert a Mac's eSATA port to USB 3 (or later, or Thunderbolt)?
There’s no easy fix here. eSATA is older, less power and slower than the items you seek to upgrade, so basically you’re putting a fancy computer in between an old port and a new device which adds cost and delays.
OWC has great support so if you asked them if they had anything they will likely agree with the assessments here.
It’s easier to take a newer, higher speed and power bus and slow it down to the older protocol as you see from your research.
The good news is you can still get eSATA storage at a discount if you are needing more speed but can’t afford a newer Mac.