I'd definitely recommend using that tank on pretty much any regulated mod over the battery it comes with. The problem is the constant 3.7v output, and with a regulated mod you can adjust the output power to find the perfect vape.
As for your issue, if barely anything is coming out but some vape is, it's making contact with the battery pin so I wouldn't worry about that just yet. What I would do first is take it apart and rinse everything out including the base. It won't hurt it. Just make sure you dry out the tank (I'm not sure if the glass on the nano will come off, but it should. That will make it easier to dry. Use a cotton swab or a rolled up tissue to dry out the base as well. To make sure with the base, open up the airflow all the way and blow through the hole the coil screws into until there's no moisture coming out (you'll see it by the airflow holes).
Put everything back together with a new coil, don't forget to prime it with a few drops on the holes and maybe a couple small ones down the middle hole. Then try it again. Floods happen, bad coils happen and it's most likely the cause of your issue.
Hope that helps.