The Parallax 7300 has been posted about on this Forum as delivering a float voltage that will boil out a battery. If you decide to keep using it with a single battery, watch the fluid levels in the battery. Don't plug in and power the converter 24/7 for days, inevitably, you will forget and your new battery will be toast.
I would suggest to replace the Parallax with a Progressive Dynamics converter, install a second battery (there is always room, somehow), and to install a battery disconnect switch.
Don't know if you're aware of this but newer TT's have alarms, circuit boards, memory hold functions that are powered 24/7 by the battery. These parasitic draws will empty even the best battery within a week if the battery is left connected. You won't be alone with this situation, nearly all TT's come built like this and the remedy would be a disconnect switch mounted close to the battery. Mfg's are too cheap to put them in.
