UA does not do one off discounts. It also won't do group bookings for <10 people. The benefits of a group booking are typically more focused on flexibility, e.g. the ability to substitute passengers than on discounts.

If LO is providing you the best price, that is what I would book. Do bear in mind that next August is so far in the future that the better discounts, e.g. lower J fare bucks will not likely open up before April-May 2020. Thus, you are paying top dollar right now.