Order also matters, so if you were to use non-background display texts/narration text action parts, take into consideration that they pause the action list in the action block that they are located in until they end/or are manually skipped.
Alternatively, you can create "called by other action" actions that you can rename & call as needed, so something you could do is create one of those & then call it just before you create the display text action part, & because it's a different action block, it should carry on in the background without waiting until the display text ends.