Okay so I solved this one myself using multiple formulae.
I started with this. That let me calculate when next Tuesday/Friday is in a way that Airtable understands.
I then created the following formula:
IF({End Date} = BLANK(),"False",
IF(AND({Next Friday}>={Start Date},{Next Friday}<DATEADD({End Date},-1,"days")),
"True", "False"))
Now I know whether an item is available Next Friday or Next Tuesday!