As others have said, to get at least some of the tickets at the lower price, you'll need to split your group into different reservations. Whether that's 4/3, 5/2, or 6/1, you need to experiment with.
Something you can TRY...
1) Open a browser, go to
Delta.com, put in your search criteria (for group 'A'), select your flight, get to the last page, put in seat selection, CC info, etc but don't click "purchase".
2) Open up another browser (or go to private/incognito mode), on the same device or a different one, go to
Delta.com, put in your search criteria (for group 'B'), select your flight, get to the last page and fill everything out.
3) Click "Purchase" on both pages as close to simultaneously as you can.
This *MIGHT* get you the same price. My theory is the second search (for group B) will still show you the lower price because group A hasn't actually claimed the seats yet.
One thing to keep in mind (and may not be a factor), any benefits held by a single person (thinking free bags or priority boarding) will only apply to the group that person is travelling with. Example: If one person has a Delta AmEx card and gets free bags, only those in their group will get that benefit. So if they're in the group of four, four people can get free bags, but the other group won't. Three people * $35/bag/one way * 2 round trip = $210 extra charge.