You're correct. DomainMarket, HugeDomains, and BuyDomains primarily sell their own inventory and aren't open marketplaces for others to list domains.
As far as I know, BrandRoot doesn't sell domains.
Could you please share your STR? And, how many names have been approved by BrandBucket or SquadHelp?
I invest in brandable domains, focusing on made-up and compound names.