The Hillsborough Family Support Group (HFSG) has organised a coach to take more than 30 families, while the Hillsborough Justice Campaign has sorted out train travel for about a dozen people.
Margaret Aspinall, the chair of HFSG, who lost her son, James, and will be attending the court, said: “I am feeling quite positive.
“There’s no decision they can make except to quash the verdicts.
“We have been disappointed in the past, but now everybody has be seen to be doing the right thing, and that is to quash the verdict.
“I am hoping the families get the good news before they travel back.”
Mr Abrahamson said he had asked for the video link to be set up to avoid a scrum of people trying to get into a packed court room.
Video could also be streamed to another room at the Royal Courts of Justice, as well as Liverpool, although it is not yet known whether it will be possible.
“It is quite clear that the court is going to want to get this done and dusted on Wednesday.”
Mr Grieve’s application is based on the findings of the Hillsborough Independent Panel, which found that 41 fans had the “potential to survive” beyond original coroner Stefan Popper’s 3.15pm cut-off point.
The main ground for the application is the new medical evidence.
A supporting factor is also the panel’s revelation that police and ambulance service statements were changed to shift blame onto fans.