Is it possible to schedule a product to go available at an 'uneven' time ?!

Site URL: http://%20www.nuligoods.com/shop

I use the "schedule" functionality so that all my products go live at a certain time, but I'd like to schedule them for, say 4:55 instead of 5:00. The built-in editor seems to only allow scheduling on the hour or half hour. 

I know this seems super minor, but it's actually really important for the way I launch product collections on Instagram. I like to have a set "release" time and since there is a bit of a delay between going live on Squarespace and your Instagram store updating, I prefer to set it a few minutes early so that when people click their Instagram notifications the products are already viewable, but not so early that anyone has a chance to shop before the set time.

Thanks in advance!