I had a suggestion from Jadon that since the V2 print had already removed the outer walls (since the box has outer walls) that I could also remove the bottom (since the box already has a bottom)! I thought this was particularly brilliant, so I threw together an example of what this would look like. For my printer, this cut off between 4 and 5 hours off the print when sliced in Cura.

I added some support between the finger holes to keep it all together and made it a little taller to account for the bottom being removed.

NOTE I haven't actually printed this (I'm happy with the V2 holder I printed), so I don't know if the 4mm support is enough to keep it all together (which is why this is a beta). If you do print this, please leave a comment or post a make so that others will know if it actually works! Jadon also suggested that I could honeycomb the sides to use even less material and time, but that's pretty advanced for me, so I might try to add it to before moving this out of Beta. Maybe I'll try it with OpenSCAD...

UPDATE #1

I uploaded a honeycombed version. I haven't tried it yet, but Cura says it can print is 6 hours and 30 minutes, this is down over 2/3 from the original version. It remains to be seen if it will have enough structural integrity!

For a tried and working Munchkin Box Holder (though slower to print), try V2