I just saw a site projecting Burnes and Hader as the Brewers representatives.
It doesn't look like Burnes will be the NL starter, but he's at least in the conversation. The other thing for him is that the Brewers could start him Tuesday and Sunday on the coming road trip, which would make him unlikely to be available at all. As a Brewer fan, I much rather have him do that, but if making an appearance in the ASG is important to him, the club might delay his next start until Wednesday (or just skip him on Sunday).
Hader certainly deserves the bid for his body of work in the first half, recent scuffling aside.
The snub would be Devin Williams. The writer of the site I saw doesn't even list him in the "snub" category, which might be an even bigger snub.
I think it's really hard to make a case for any of the position players/DHs.