That might explain the Launchbox issue. I use the same devices. For the tankstick I assume you are using standard keyboard inputs? If so, in Launchbox, the Tankstick will not work as you can only set 1 keyboard input for pause. So if in Launchbox it is set to "P" and not a key your tankstick can trigger Mame will not Pause to the Launchbox Pause Menu. It will only pause directly in Mame. In BigBox it should work because you can set a combo and it will send "P" to Mame.
What do you use to initiate Pause on the Tankstick.