Oh, and also: the picker has more purposes than just selecting the target to use for tasks. It also changes the code completion arguments. This is necessary for completion to work properly for platform-specific APIs and conditional compilation blocks like #if js.
And you don’t have to click around in the UI, everything is bound to commands you can assign shortcuts to. I have this in my keybindings.json:
{
"key": "ctrl+e",
"command": "haxe.selectDisplayConfiguration",
"when": "haxeCompletionProvider == 'Haxe'"
},
{
"key": "ctrl+e",
"command": "lime.selectTarget",
"when": "haxeCompletionProvider == 'Lime'"
}