I have actually made exactly this in the past, but nothing that could be shared unfortunately.
The way you want to do this is to make a single template for how you want everything displayed in a tiddler and then transclude that into the tiddler where you want it displayed.
For the stats block in particular you would make a tiddler called StatsBlockTemplate (or whatever you want to name it) with something like this in the text field:
!!!''STATS:''
|Name: {{!!name}} |h
|''Attributes:'' |Agility: {{!!agility}} | Smarts: {{!!smarts}} | Spirit: {{!!spirit}} | Strength: {{!!strength}} | Vigor: {{!!vigor}} |h
|''Skills:'' | {{!!skills}} |h
|Charisma: |Pace: |Parry: {{!!parry}} |Toughness: {{!!toughness}} |h
|Hinderances: | {{!!hinderances}} |h
|Edges: | {{!!edges}} |h
|Booty: | {{!!booty}} |h
|Gear: | {{!!gear}} |h
You probably also want to give it a field called 'caption' with a value 'Stats Block', this is what will be displayed on the tab.
Then you make a tiddler for each character, and in those tiddlers you create fields for each attribute, like name, agility, etc. and in that tiddler you put <<tabs "StatsBlockTemplate">>
and it will display the stats block in a tab, but the values for each attribute will be taken from the containing tiddler. Then you can do the same thing for the other tabs. This way you can have all of your character data in a single tiddler and control how it is displayed using the other templates.
To make this easier you can tag the tiddler will all of the character information with Character, then make a conditional view template that automatically displays the information tabs in that tiddler also.