Slow-feed Horse Hay Bags for Goats????

[Sanhestar]

If you are really worried about entanglement during transport you could also check out if a hay toy/hay ball is something your goats can accept during transport.

https://www.reitshop24.de/kerbl-heuboy-f...87EALw_wcB

Round Balls to be put into a holder of some kind to keep them from rolling on the floor during the drive.

HayToys for horses sometimes come in the form of barrels with holes cut into them. You could use smaller barrels or another, largish plastic container.

https://www.udoroeck.de/heutoy-home

these are German sites, just to give you some ideas.